LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

Class 


Y' 
v 


V 

v 


4? 

y, 


C0lum6ta 


LI&HT 

THE  JESUP  LECTURES 
190a-1909 


NEWTON 


COLUMBIA    UNIVERSITY  LECTURES 


LIGHT 


BY 


RICHARD   C.   MACLAURIN,  LL.D.,  Sc.D, 

PRESIDENT   OF   THE  MASSACHUSETTS   INSTITUTE 
OF   TECHNOLOGY 


OF  THE 

UNIVERSITY 

OF 


Nefo 
THE  COLUMBIA  UNIVERSITY  PRESS 

1909 

All  rights  reserved 


COPTBIGHT,   1909, 

BY  THE  COLUMBIA  UNIVERSITY  PRESS. 
Set  up  and  electrotyped.    Published  June,  1909. 


J.  8.  Gushing  Co.  —  Berwick  <fe  Smith  Co. 
Norwood,  Mass.,  U.S.A. 


PREFACE 

THESE  lectures  were  given  at  the  American  Museum  of 
Natural  History  during  the  winter  of  1908-9,  when  I  had 
the  honor  of  occupying  a  chair  of  Mathematical  Physics 
at  Columbia  University  in  the  City  of  New  York.  It  is 
not  easy,  in  such  a  place,  for  a  man  of  science  to  sit  in 
cloistered  calm,  far  from  the  distractions  of  the  busy 
world  of  action,  and  to  pursue  research  merely  for  self- 
illumination  or  for  the  edification  of  a  caste  of  intel- 
lectuals. The  throb  of  life  is  all  around  him,  and  it 
impresses  him  with  the  duty  of  responding  to  the  de- 
mands of  an  active-minded  people  for  reliable  informa- 
tion on  the  most  recent  developments  of  science.  He  is 
expected  to  know  ;  but  not  only  to  know,  but  also  to 
communicate.  And  so,  on  being  invited  to  give  the  Jesup 
Lectures,  I  attempted  to  describe  the  salient  features  of 
the  modern  theory  of  light  within  the  narrow  compass  of 
ten  lectures,  and  undertook  in  doing  so  to  avoid  techni- 
calities as  much  as  possible.  I  have  had  specially  in  view 
the  man  of  intelligence  who  lays  no  claim  to  scientific 
knowledge,  but  who  wishes  to  know  what  all  the  talk  of 
science  is  about,  and,  in  particular,  why  the  physicists 
make  such  strange  postulates  as  ether  and  electrons,  and 
why  they  have  so  much  confidence  in  the  methods  that 
they  employ  and  the  results  that  they  obtain.  For  this 
purpose  I  have  had  to  show  him  how  wonderfully  the 
theory  fits  the  facts,  down  to  the  minutest  numerical 


193277 


yi  PREFACE 

detail;  although,  of  course,  the  full  force  of  the  argument 
is  lost  owing  to  the  necessity  of  eschewing  mathematics 
and  merely  stating  the  results  of  theory  without  giving 
the  actual  demonstrations,  except  in  the  simplest  cases. 
I  hope,  too,  that  the  book  may  be  found  useful  to  the 
large  body  of  teachers  of  physics  throughout  the  country. 
They  will  find  in  it  much  that  is  scarcely  touched  upon  in 
the  ordinary  text-books,  and  their  appreciation  of  the  dif- 
ficulties of  presenting  such  a  subject  in  non-technical  lan- 
guage will  put  them  in  that  sympathetic  frame  of  mind 
that  helps  so  much  towards  the  understanding  of  a  writer. 
My  thanks  are  due  to  Mr.  Farwell  for  the  care  and 
skill  with  which  he  conducted  the  experiments  that  illus- 
trated the  lectures,  and  to  my  colleague,  Professor  E.  F. 
Nichols,  for  reading  the  proof-sheets  and  displaying  a 
keen  interest  in  the  progress  of  the  course. 

R.  C.  M. 


"  A  man  of  science  does  well  indeed  to  take  his  views  from 
many  points  of  sight,  and  to  supply  the  defects  of  sense  by  a 
well-regulated  imagination;  but  as  his  knowledge  of  Nature 
is  founded  on  the  observation  of  sensible  things,  he  must  be- 
gin with  these,  and  must  often  return  to  them  to  examine  his 
progress  by  them.  Here  is  his  secure  hold  ;  and,  as  he  sets 
out  from  thence,  so  if  he  likewise  trace  not  often  his  steps 
backwards  with  caution,  he  will  be  in  hazard  of  losing  his 
way  in  the  labyrinths  of  Nature."  —  Colin  Maclaurin :  An 
account  of  Sir  Isaac  Newton's  Philosophical  Discoveries. 
(1748.) 


vii 


CONTENTS 


LBOTtTKl!  PAGE 

I.  EARLY  CONTRIBUTIONS  TO  OPTICAL  THEORY       .        .        1 

II.  COLOR  VISION  AND  COLOR  PHOTOGRAPHY    ...      24 

III.  DISPERSION  AND  ABSORPTION 47 

IV.  SPECTROSCOPY Y       .        .70 

V.  POLARIZATION  .        ....        ,        .        *        •      95 

VI.    THE  LAWS  OF  REFLECTION  AND  REFRACTION  .  .    118 

VII.    THE  PRINCIPLE  OF  INTERFERENCE        .        ,  .  .    154 

VIII.     CRYSTALS  .        .        .        .        .      :;  V  "  •  .»'      .  '  .  .     175 

IX.    DIFFRACTION     .        .        .*     .        .        .        .  .  .202 

X.     LIGHT  AND  ELECTRICITY         .       V       .        .  .  .    229 

INDEX  249 


LIGHT 


EARLY   CONTRIBUTIONS  TO   OPTICAL  THEORY 

"THEY  tell  us,"  said  Matthew  Arnold,  "that  when  a 
candle  burns,  the  oxygen  and  nitrogen  of  the  air  combine 
with  the  carbon  in  the  candle  to  form  carbonic  acid  gas.  — 
Who  cares?"  I  recall  the  story  not  with  the  object  of 
revealing  flaws  in  the  chemistry  of  the  brilliant  advocate 
of  sweetness  and  of  light,  but  because  it  suggests  an  atti- 
tude to  science  that  is  far  from  rare,  even  amongst  people 
of  intelligence  to-day.  They  tell  you,  sometimes  frankly, 
but  more  often  by  implication,  that  they  care  for  none  of 
these  things.  Perhaps  it  is  worth  considering  for  a  moment 
to  what  this  attitude  is  due.  Doubtless  it  springs  from  a 
variety  of  causes,  according  to  the  infinitely  varied  con- 
stitutions of  the  minds  and  hearts  of  the  different  thinkers ; 
but  in  nine  cases  out  of  ten  its  origin  can,  I  think,  be 
traced  either  to  misconception  or  to  ignorance.  Men  are 
engrossed  in  other  affairs;  they  know  of  science  only  by 
scraps,  an  occasional  lecture,  perhaps,  or  a  magazine  article 
read  to  lessen  the  tedium  of  a  railroad  journey.  At  the 
best  they  get  a  sight  only  of  a  portion  of  any  one  science, 
never  a  clear  view  of  the  whole  structure.  Now  modern 
science  is  an  elaborate  work  of  art,  and  to  be  thoroughly 
appreciated  it  must  be  looked  upon  as  a  whole.  Who  that 

B  1 


2  LIGHT 

has  any  eye  and  mind  for  the  beautiful,  and  that  finds 
himself  in  the  presence  of  a  great  master,  such  as  Rem- 
brandt, will  rest  content  with  so  distant  a  view  or  so  hur- 
ried a  glance  that  he  can  see  only  the  outline  of  a  hand  or 
the  contour  of  a  cloak?  The  mind  that  can  really  carry 
out  the  process  suggested  by  the  phrase  ex  pede  Hercukm 
is  not  only  rarely  gifted,  but  must  have  been  trained  with 
unusual  care.  In  a  million,  not  ten  that  see  only  the  foot 
will  have  anything  but  the  vaguest  vision  of  the  whole  man 
Hercules.  The  rest  will  turn  aside  with  apathy  and  mur- 
mur, "Who  cares?'7 

Bearing  these  facts  in  mind  in  this  course  of  lectures  on 
Light,  I  shall  try  to  give  you  something  more  than  a  glimpse 
or  two  of  single  portions  of  the  great  scientific  structure. 
Our  view  must  necessarily  be  very  incomplete,  for  to  visit 
every  portion  of  the  building  and  study  it  with  thoroughness 
would  require  the  devotion  of  a  lifetime.  At  the  best  I 
can  take  you  along  the  corridors  and  let  you  see  into  some 
of  the  principal  rooms.  Enough,  I  hope,  to  enable  you  to 
grasp  the  main  features  of  the  plan  and  to  put  you  in  a 
position  to  appreciate  the  genius  of  the  architects,  and  to 
realize  something  of  the  patience  and  endurance  required 
to  overcome  so  many  obstacles  and  to  build  so  solidly  and 
well.  If,  however,  there  is  any  here,  as  I  sincerely  hope 
there  is,  who  craves  for  more  than  this,  and,  not  content 
with  general  outlines,  wishes  to  probe  into  the  very  heart 
of  nature,  then,  although  I  wish  him  all  joy  and  success 
in  his  quest,  I  think  it  right  to  warn  him  that  he  must  not 
expect  very  much  from  such  a  course  as  this.  As  Euclid 
said  to  the  Egyptian  king  inquiring  for  a  short  cut  to  the 
mastery  of  geometry,  "Sire,  there  is  no  royal  road 
thereto."  Indeed,  hard  is  the  road  and  narrow  the  way, 


EARLY  CONTRIBUTIONS  TO  OPTICAL  THEORY         3 

and  to  follow  it  to  the  end  requires  a  clear  head,  and  above 
all  a  stout  heart.  At  the  best  I  can  put  you  on  the  way. 

I  have  suggested  that  some  men  turn  away  from  science 
through  the  mere  scrappiness  of  their  knowledge,  but  this 
is  not  the  only  thing  that  renders  its  pursuit  unattractive. 
Many  poetic  natures  find  it  cold  and  inhuman.  Recall 
the  query  of  Keats :  — 

"  Do  not  all  charms  fly 
At  the  mere  touch  of  cold  philosophy  ? 
There  was  an  awful  rainbow  once  in  heaven ; 
We  know  her  woof  and  texture.    She  is  given 
In  the  dull  catalogue  of  common  things." 

The  complaint  seems  to  be  that  science,  with  its  cold 
analysis,  robs  us  of  the  pleasing  sense  of  awe  and  mystery  ; 
but  if  you  dig  deep,  you  will  find  still  enough  of  mystery 
left  to  satisfy  the  keenest  yearner  after  half  lights  and  the 
obscure.  At  the  best,  science  only  replaces  one  mystery 
by  another  of  grander  order. 

As  to  the  alleged  inhumanity  of  science,  the  charge  is 
probably  made  by  way  of  protest  against  the  attitude  of 
some  who,  in  the  generation  just  past,  made  exaggerated 
claims  in  the  name  of  science.  They  professed  to  worship 
Nature  and  to  worship  her  so  jealously  as  not  to  tolerate 
the  worship  of  any  other  gods  besides.  They  disparaged 
those  human  studies  that  have  occupied  men's  minds 
throughout  the  ages,  and  were  so  far  from  believing  that 
"the  proper  study  of  mankind  is  man  "  as  to  give  the  im- 
pression that  that  was  the  one  kind  of  study  not  worth 
pursuing. 

Such  extreme  opinions  are  naturally  resented  by  the 
Humanists,  who  hold  that  "man  hath  all  which  Nature 


4  LIGHT 

hath;  but  more,  And  in  that  more  lie  all  his  hopes  of  good." 
The  controversy  is  fortunately  dead  by  this  time,  when 
science  has  become  more  genial,  and  it  is  seen  to  be  absurd 
to  make  an  arbitrary  separation  between  man  and  nature. 
Apart  from  this,  it  is  an  obvious  truism  that  a  science  such 
as  that  of  light  is  a  purely  human  study;  it  is  taken  up 
with  discussions  as  to  what  man  has  thought  of  one  of  the 
most  impressive  of  his  sensations,  so  that  the  study  of 
its  history  proves  of  intensely  human  interest.  Here  we 
watch  the  race  grappling  with  great  intellectual  difficul- 
ties, and  we  see  the  spectacle  of  her  champions  painfully 
but  surely  overcoming  countless  obstacles.  Each  of  their 
victories  is  a  genuine  victory  of  the  spirit,  each  of  their 
defeats  a  spiritual  chastisement. 

Others  who  stop  short  of  charging  science  with  inhuman- 
ity, think  that  its  study  robs  men  of  their  natural  powers 
of  appreciation.  They  point  to  the  pathetic  case  of  Darwin, 
but  it  would  tie  easy  to  quote  many  great  names  to  show 
that  Darwin's  experience,  even  if  it  has  not  been  misunder- 
stood, is  extremely  unusual.  It  would  indeed  be  a  terrible 
price  to  pay  for  our  exact  knowledge  of  optics,  if  it  robbed 
us  of  our  due  joy  in  color  and  in  light.  Fortunately, 
however,  there  is  not  the  slightest  reason  why,  after  pon- 
dering over  the  laws  of  light,  we  should  appreciate  less  the 
brilliance  of  a  New  York  sky  or  the  glory  of  the  autumn 
tints  in  the  woods  around  us.  Our  study  should  rather 
increase  our  interest  and  our  capacity  for  appreciation  and 
enjoyment.  It  is  strangely  true,  however,  that  artists 
have  often  an  antipathy  to  the  science  —  and  this  in  spite 
of  the  fact  that  the  problems  that  they  have  to  face  require 
for  their  solution  an  accurate  knowledge  of  many  optical 
laws.  Few  men  knew  better  than  Ruskin  that  between 


EARLY  CONTRIBUTIONS  TO  OPTICAL  THEORY         5 

wise  art  and  wise  science  there  is  essential  relation  for  each 
other's  help  and  dignity,  and  yet  even  he  seems  doubtful 
as  to  the  benefit  of  scientific  knowledge  to  the  artist.  His 
lecture  on  the  relation  to  art  of  the  science  of  light  is  un- 
usually diffuse  (it  deals  almost  as  much  with  snakes  as  with 
either  art  or  science),  so  that  it  is  difficult  to  gather  here 
anything  relevant  to  the  present  discussion.  In  another 
place,  however,  he  says  plainly  that  scientific  knowledge 
may  be  positively  harmful  to  the  artist.  "The  knowledge 
may  merely  occupy  the  brain  wastefully  and  warp  his 
artistic  attention  and  energy  from  their  point.  As  an 
instance,  Turner,  in  his  early  life,  was  sometimes  good- 
natured,  and  would  show  people  what  he  was  about.  He 
was  one  day  making  a  drawing  of  Plymouth  harbor, 
with  some  ships  at  the  distance  of  a  mile  or  two,  seen 
against  the  light.  Having  shown  this  drawing  to  a  naval 
officer,  the  naval  officer  observed  with  surprise,  and  ob- 
jected with  very  justifiable  indignation,  that  in  the  picture 
the  ships  of  the  line  had  no  port-holes.  'No/  said  Tur- 
ner, '  certainly  not.  If  you  will  walk  up  to  Mt.  Edge- 
comb,  and  look  at  the  ships  against  the  sunset,  you  will 
find  that  you  can't  see  the  port-holes.'  '  Well,  but/  said 
the  naval  officer,  still  indignant,  'you  know  the  port-holes 
are  there.'  'Yes/  said  Turner,  'I  know  that  well  enough; 
but  my  business  is  to  draw  what  I  see,  and  not  what  I  know 
is  there.'"  This  is  doubtless  true  enough,  but  its  chief 
application  in  Ruskin's  mind  had  reference  to  the  science  of 
anatomy,  the  study  of  which,  he  thought,  had  spoilt  many 
a  good  artist  by  giving  him  the  "butcher's  view."  It 
can  scarcely,  however,  be  applicable  to  Light,  for  that 
artist  has  yet  to  arise  who  is  so  imbued  with  optical  theories 
as  to  distinguish  blue  from  red  by  drawing  ether  waves 


6  LIGHT 

of  the  different  lengths  that  science  postulates.  Probably 
the  repulsion  of  the  artist  to  the  science  of  light  is  due,  at 
least  in  part,  to  the  feeling  that  the  splendor  of  light  and 
color  has  little  to  do  with  the  mechanical  concepts  of 
optical  theory ;  but  although  modern  science  is  accustomed 
to  speak  hi  the  language  of  mechanics,  it  is  quite  prepared 
to  admit  that  the  artist's  feeling  may  be  entirely  an  affair 
of  the  spirit.  It  would  like  to  see  all  artists  walking  in 
its  ranks.  Of  course  no  one  would  seriously  suggest  that 
the  study  of  optical  science  will  make  you  an  artist.  If, 
however,  you  have  the  artistic  spirit,  you  will  understand 
that  the  science  of  Light  is  really  a  work  of  conscious  and 
premeditated  art.  Your  intelligence  will  urge  you  to  know 
at  least  something  about  the  subject,  and  you  may  even 
agree  with  Ruskin  that  "whatever  it  is  really  desirable 
and  honorable  to  know,  it  is  also  desirable  and  honorable  to 
know  as  completely  as  possible." 

If  you  will  permit  me  one  word  more  of  an  introductory 
character,  I  should  like  to  say  that  it  will  be  my  endeavor 
to  present  the  subject  with  all  possible  simplicity.  This, 
I  hope,  needs  no  apology ;  at  any  rate  you  will  not  suppose 
that  I  underrate  your  powers  if  I  try  to  make  things  as 
easy  as  I  can.  Of  course  it  is  true,  as  Ruskin  says,  that 
"no  study  that  is  worth  pursuing  seriously  can  be  pursued 
without  effort" ;  but  it  is  needless  to  make  the  effort  painful 
merely  for  the  sake  of  preserving  our  dignity.  And  while 
I  shall  avoid  technicalities  as  much  as  possible  for  the 
sake  of  lucidity,  for  the  sake  of  art  I  shall  equally  avoid 
any  attempt  at  word-painting.  The  subject  is  too  great  in 
itself  for  anything  but  a  studied  simplicity  in  its  treatment. 

The  theory  of  light  has,  in  these  latter  days,  achieved 
so  many  successes,  and  been  worked  up  into  so  nearly 


EARLY  CONTRIBUTIONS  TO  OPTICAL  THEORY         7 

perfect  a  form,  that  there  is  a  temptation  to  forget  the 
labors  of  the  great  men  of  the  past  who  have  done  so  much 
to  make  these  modern  victories  possible,  and  to  present  the 
theory  in  the  form  it  bears  to-day  as  if  no  other  had  been 
thought  of.  It  is  a  temptation  to  be  rigorously  withstood. 
In  science  no  less  than  in  other  branches  of  human  activity 
we  must  not  allow  ourselves  to  forget  that  the  roots  of  the 
present  lie  deep  in  the  past.  By  so  doing  we  neglect  a 
valuable  aid  to  the  thorough  understanding  of  the  present, 
and  we  rob  ourselves  of  the  pleasure  and  the  illumination 
that  comes  from  tracing  the  development  through  the  ages 
of  a  great  idea.  Unfortunately,  in  the  present  lectures  we 
shall  have  no  time  for  this,  but  we  can  scarcely  avoid  dip- 
ping a  little  into  the  past,  even  in  the  most  cursory  examina- 
tion of  optical  theory. 

Doubtless  thoughtful  men  of  various  races  must  have 
pondered  over  the  phenomena  of  light,  but  amongst  the 
earliest  references  in  literature  to  anything  that  can,  by  the 
utmost  stretching  of  terms,  be  dignified  by  the  name  of  a 
theory  of  light,  are  the  speculations  of  some  of  the  philoso- 
phers of  Greece.  The  Greek  mind  is  so  often  and  so  justly 
held  up  as  an  object  of  admiration  that  it  is  with  something 
of  a  shock  that  we  read  the  puerilities  of  its  greatest  thinkers 
when  dealing  with  physical  science.  In  the  field  of  optics 
they  seem  mainly  to  have  been  occupied  with  the  question 
whether  objects  become  visible  by  means  of  something 
emitted  by  them,  or  by  means  of  something  that  issues  from 
the  seeing  eye.  Five  centuries  B.C.  Pythagoras  and  his 
school  held  that  vision  is  caused  by  particles  continually 
projected  into  the  pupil  of  the  eye;  while  later,  Empedocles 
maintained  that  to  excite  the  sense  of  sight  there  must 
be  something  emitted  from  the  eye,  and  that  this  must 


8  LIGHT 

meet  with  something  else  proceeding  from  the  object  seen. 
Listen  to  and  get  what  enlightenment  you  can  from 
Plato's  explanation  of  an  act  of  vision:  — 

"The  pure  fire  that  is  within  us  the  gods  made  to  flow 
through  the  eyes  in  a  single  smooth  substance,  at  the  same 
time  compressing  the  center  of  the  eye  so  as  to  retain  all 
the  denser  element,  and  only  to  allow  this  to  be  sifted 
through  pure.  When,  therefore,  the  light  of  day  surrounds 
the  stream  of  vision,  then  like  falls  upon  like,  and  there  is  a 
union,  and  a  body  is  formed  by  natural  affinity,  according  to 
the  direction  of  the  eyes,  wherever  the  light  that  falls  from 
within  meets  that  which  comes  from  an  external  object. 
And,  everything  being  affected  by  likeness,  whatever  touches 
and  is  touched  by  this  stream  of  vision,  their  motions  are 
diffused  over  the  whole  body,  and  reach  the  soul,  producing 
that  perception  which  we  call  sight.  But  when  the  external 
and  kindred  fire  passes  away  in  night,  then  the  stream  of 
vision  is  cut  off;  for,  going  forth  to  the  unlike  element,  it  is 
changed  and  extinguished,  being  no  longer  of  one  nature 
with  the  surrounding  atmosphere,  which  is  now  deprived 
of  fire :  the  eye  no  longer  sees,  and  we  go  to  sleep ;  for  when 
the  eyelids  are  closed,  which  the  gods  invented  as  the  pres- 
ervation of  the  sight,  they  keep  in  the  eternal  fire."  So 
much  for  his  explanation  of  vision.  Hear  next  his  theory 
of  colors.  "There  is  a  class  of  sensible  things  called  by  the 
general  name  of  colors.  They  are  a  flame  that  emanates 
from  all  bodies,  a  flame  that  has  particles  corresponding  to 
the  sense  of  sight.  Of  the  particles  coming  from  other 
bodies  that  fall  upon  the  sight,  some  are  less,  some  are 
greater,  and  some  are  equal  to  the  parts  of  the  sight  itself. 
Those  that  are  equal  are  imperceptible,  or  transparent,  as 
we  call  them,  whereas  the  smaller  dilate,  the  larger  contract 


EARLY  CONTRIBUTIONS  TO  OPTICAL  THEORY         9 

the  sight,  having  a  power  akin  to  that  of  hot  and  cold  bodies 
on  the  flesh,  or  of  astringent  bodies  on  the  tongue.  Those 
that  dilate  the  visual  ray  we  term  white,  the  others  black." 
Aristotle,  of  course,  objected  to  this  as  to  most  of  Plato's 
science.  He  came,  in  a  vague  way,  nearer  to  the  modern 
view,  as  he  regarded  light  not  as  material  at  all,  but  as 
the  influence  of  a  medium  on  the  eye.  He  says :  "  Vision 
is  the  result  of  some  impression  made  upon  the  faculty 
of  sense,  an  impression  that  must  be  due  to  the  medium 
that  intervenes.  There  exists  something  which  is  pellucid. 
Light  is  the  action  of  this  pellucid,  and  whenever  this 
pellucidity  is  present  only  potentially,  there  darkness  also 
is  present.  Light  is  neither  fire  nor  substance,  but  only 
the  presence  of  fire,  or  something  like  it,  in  that  which  is 
pellucid."  This  is,  I  think,  the  clearest  account  we  have  in 
Greek  philosophy  of  the  nature  of  light.  I  will  not  venture 
to  say  that  it  is  obscure,  but  perhaps  I  may  be  permitted 
to  use  Aristotle's  own  phraseology,  and  suggest  that  "its 
pellucidity  is  present  only  potentially." 

However,  I  must  not  weary  you  further  with  the  specu- 
lations of  Greek  philosophers  or  medieval  thinkers.  It  is 
not  until  the  seventeenth  century  of  our  era  that  we  get 
any  really  great  advance,  when  Snell  discovered  the  law  of 
refraction  and  Newton  made  his  classical  experiments  on 
color.  We  may  well  pause  just  for  a  moment  to  consider 
why  in  all  those  ages  the  world  of  science  stood  so  still. 
Certainly  it  was  not  due  to  any  lack  of  intellect.  No  one 
who  looks  into  the  matter  can  fail  to  recognize  that  there 
really  were  giants  of  old.  Indeed  it  would  be  a  hazardous 
thing  to  assert  that  within  the  last  two  thousand  years  there 
is  any  evidence  of  human  advancement,  if  you  measure  man 
merely  by  the  intellectual  power  of  the  greatest  of  his  kind. 


10  LIGHT 

Talk  with  an  ancient  or  medieval  philosopher  on  matters 
of  science,  and  he  appears  like  a  child;  but  take  him  on 
his  own  ground,  and  you  will  have  to  wrestle  hard  indeed  to 
overthrow  him.  No,  it  is  not  in  mind  but  in  method  that 
the  race  has  advanced ;  and  where  we  are  superior  to  our 
forefathers  is  in  the  fact  that  we  have  learned  —  at  any 
rate  in  science  —  first  to  lay  a  solid  foundation  of  fact  before 
we  begin  to  theorize. 

If  you  search  in  the  field  of  optics,  you  will  find  that  the 
only  general  facts  known  before  the  seventeenth  century 
could  all  be  stated  in  a  few  minutes.  They  were  these :  — 

(1)  Light  travels  in  straight  lines  —  a  partial  truth  that 
proved  to  be  more  misleading  than  a  lie.  (2)  The  fact 
and  the  law  of  reflection.  (3)  The  fact  of  refraction  — 
not  its  law.  (4)  The  fact  of  total  reflection.  These  things 
are  probably  familiar  to  most  of  you;  but  for  the  sake  of 
those  to  whom  they  are  not,  it  may  be  well  to  direct  your 
attention  to  a  few  simple  experiments,  so  that  all  may 
realize  clearly  how  much  and  how  little  was  known  in  the 
good  old  days.  In  the  first  place,  "  light  appears  to  move 
in  straight  lines."  This  is  familiar  to  every  one  who  has 
looked  at  a  shadow  and  noticed  that  its  contour  is  deter- 
mined by  drawing  straight  lines  from  the  source  of  light  past 
the  edges  of  the  object  that  casts  the  shadow.  The  light 
goes  straight  past  the  edge  and  does  not  bend  round  corners, 
so  that  we  are  tempted  to  lay  down  the  law  that "  light  moves 
in  straight  lines."  The  one  objection  is  that  it  is  not  true. 
As  we  shall  see  later,  this  is  a  case  in  which  we  are  misled 
by  our  senses.  Light  does  bend  round  corners,  but  under 
ordinary  circumstances  the  bending  is  so  slight  that  the  eye 
is  unable  to  detect  it.  So  much  for  one  of  the  four  general 
principles  known  before  the  seventeenth  century.  The 


EARLY  CONTRIBUTIONS  TO  OPTICAL  THEORY       11 

other  three  can  all  be  demonstrated  by  slight  modifications 
of  the  same  experiment.  Darken  your  room  as  much  as 
possible,  and  let  light  from  the  sun  stream  in  through  a 
single  chink.  (If  you  prefer  to  work  at  night,  you  can  make 
an  artificial  light  take  the  place  of  the  sun.)  Let  this 
light  fall  on  a  tumbler  of  water  in  which  are  two  or  three 
drops  of  milk.  Blow  in  a  little  smoke  to  show  the  path  of 
the  ray,  or  scatter  a  little  powder,  if  you  object  to  smoke. 
You  will  observe  that  the  ray,  when  it  strikes  the  surface 
of  the  water,  is  bent  back  into  the  air.  This  is  the  fact 
of  reflection.  Its  law  is  that  the  incident  and  reflected  rays 
are  equally  inclined  to  the  surface  of  the  water,  and  this  also 
you  can  verify.  If  you  are  interested  only  in  reflection, 
it  will  be  better  to  use  an  ordinary  mirror  rather  than  the 
water  to  produce  reflection,  as  thereby  you  will  get  more 
light  reflected,  and  will  have  less  difficulty  in  seeing  the 
reflected  beam  distinctly.  The  advantage  of  the  water  is 
that  it  enables  you  to  observe  the  other  phenomena,  to 
which  reference  has  been  made.  You  will  see  that  not  all 
the  light  is  reflected,  but  that  there  is  a  bright  beam  in 
the  water.  This  beam  is  not  in  the  same  direction  as  the 
incident  one ;  it  looks  as  if  the  beam  were  broken  at  the  sur- 
face. This  is  the  fact  of  refraction;  the  law  that  enables 
us  to  predict  exactly  how  much  it  will  be  broken  was  not 
yet  known  at  the  time  of  which  I  speak.  In  this  experi- 
ment you  have  allowed  the  light  to  strike  the  water  from 
above.  By  means  of  a  reflecting  mirror  it  is  easy  to  make 
it  reach  the  water  surface  from  below.  If  you  do  this,  you 
will  again  get  the  phenomena  of  reflection  and  refraction; 
but  as  you  vary  the  angle  at  which  the  ray  strikes  the  sur- 
face, you  will  come  to  a  region  where  the  refracted  ray 
disappears.  All  the  light  is  then  reflected.  This  is  the 


12 


LIGHT 


phenomenon  of  totd  reflection,  and  here  again  the  fact,  but 
not  the  law,  was  known  before  the  seventeenth  century. 
Before  making  these  experiments,  it  may  be  well  to  look  at 
Fig.  1,  which  indicates  what  is  to  be  expected. 


FIG.  1 

The  line  SBS'  represents  a  section  of  the  surface  of  the 
water  in  the  glass  tank  that  stands  upon  this  table.  AB 
is  a  beam  of  light  from  the  lantern,  and  when  this  strikes 
the  water  at  B,  part  of  it  is  reflected  along  BC  and  part 
refracted  along  BE.  The  line  A'B'C'D'  represents  the 
path  of  the  beam  when  things  are  arranged  to  exhibit  the 
phenomenon  of  total  reflection.  A  beam  A  'B'  from  the 
lantern  is  reflected  along  E'C'  by  a  plane  mirror  at  B1 '. 
When  the  angle  at  which  it  strikes  the  water  surface  SS' 
is  properly  chosen,  the  whole  of  the  light  is  reflected  along 
C'D'. 

I  will  now  ask  Mr.  Farwell  to  show  you  these  experi- 
ments, not  because  they  are  novel  or  beautiful,  but  partly 
because  they  deal  with  fundamental  facts,  and  partly  be- 
cause I  want  to  bring  home  to  you  the  striking  fact  that 
the  results  of  human  thinking  over  the  phenomena  of  light 
for  thousands  of  years  before  the  seventeenth  century  of  our 
era  can  all  be  presented  in  a  single  minute.  How  little 
these  thinkers  really  knew !  To  those  of  you  who  are 
familiar  with  the  immense  field  of  modern  optics,  the  omis- 


EARLY  CONTRIBUTIONS  TO  OPTICAL  THEORY       13 

sions  will  appear  enormous.  The  one  that  I  wish  to  em- 
phasize to-night  is  the  absence  of  any  exact  knowledge 
and  any  feasible  theory  of  color.  Its  absence  is  the  more 
striking,  as  color  is  an  attribute  of  light  that  impresses 
not  only  the  artist  and  the  man  of  science,  but  every 
normal  human  being.  The  man  who  unlocked  this  secret 
was  he  who  is  everywhere  hailed  as  the  greatest  of  all 
physicists,  the  man  whose  achievements  so  changed  the 
current  of  men's  thoughts  as  to  form  the  Great  Divide,  in 
the  realm  of  science,  between  the  ancient  and  the  modern 
world  —  Isaac  Newton.  You  know  that  his  greatest 
achievements  were  in  other  fields,  yet  even  in  the  domain 
of  optics  I  must  to-night  confine  myself  to  a  very  small  por- 
tion of  what  he  did,  but  that  portion  was  epoch-making. 

I  hold  in  my  hand  his  little  book  on  "Opticks."  Turn 
over  its  pages,  and  you  will  be  struck  by  the  style.  The 
writer  has  evidently  been  brought  up  in  the  strict  school 
of  the  geometers,  with  Euclid  for  his  model.  Here  is  no 
collection  of  obscure  musings  and  hazy  speculations,  but 
clear  statements  of  what  is  to  be  proved  and  the  manner 
of  proving  it.  After  some  preliminary  definitions,  the  book 
proceeds  thus :  — 

"Proposition  I.  Theorem  I.  Light  which  differs  in 
color  differs  also  in  degrees  of  Refrangibility."  Then 
follows  the  proof.  "Prop.  II.  Theor.  II.  The  light  of 
the  Sun  consists  of  Rays  differently  Refrangible."  And 
so  on.  Notice  most  carefully  that  he  does  not  tread  the 
old  high  a  priori  road.  He  is  not  content,  like  many  a 
philosopher  before  and  since,  to  sit  in  an  obscure  study  and 
think.  He  also  observes.  Listen  to  the  first  sentence  of 
his  book.  "My  design  in  this  book  is  not  to  explain  the 
properties  of  light  by  hypotheses,  but  to  propose  and  prove 


14  LIGHT 

them  by  reason  and  experiments."  That  is  the  combination 
that  tells  —  reason  and  experiment.  Neither  is  of  much 
use  without  the  other.  We  have  seen  where  reason  alone 
landed  the  greatest  thinkers  of  the  ancient  world,  and 
experiment  alone  would  have  been  equally  futile.  To 
advance  science  by  experiment  is  no  haphazard  process, 
as  some  imagine.  It  is  a  supreme  effort  of  the  mind,  re- 
quiring imagination  and  a  working  hypothesis  to  make  it 
effective.  Without  this  the  experimenter  does  not  know 
what  questions  to  put  to  Nature.  Compare  a  skilful  cross- 
examiner  in  the  law  courts  with  a  novice.  The  latter  asks 
questions  at  random,  in  the  hope  (generally  a  vain  one) 
that  he  may  hit  on  something  relevant.  The  former  has 
a  theory  and  a  consequent  method. 

The  experiments  that  Newton  describes  to  prove  his 
various  propositions  are  very  numerous.  As  time  is  short, 
we  must  to-night  select  a  very  few.  Those  of  you  who  are 
really  interested  will  doubtless  repeat  most  of  Newton's 
experiments  for  yourselves.  I  expect  that  you  could  buy 
the  necessary  outfit  at  one  of  those  marvels  of  New  York  — 
a  ten-cent  shop.  The  apparatus  is  certainly  wonderfully 
simple,  consisting  usually  of  little  more  than  a  glass  prism, 
and  this  fact  may  suggest  the  query  why,  in  this  wiser  age, 
such  costly  machinery  is  required  to  produce  much  less 
epoch-making  results.  The  answer  is  that,  by  the  labors  of 
men  like  Newton  and  their  followers,  science  has  advanced  so 
rapidly  and  has  become  so  much  more  exact  that  instruments 
of  precision,  generally  costly,  are  needed  to  move  forward, 
where  rougher  tools  would  have  availed  before.  Newton's 
first  proposition  is  that  "  Lights  that  differ  in  color  differ 
also  in  degrees  of  refrangibility."  The  fact  of  refraction 
has  already  been  brought  before  you.  You  have  seen  that 


EARLY  CONTRIBUTIONS  TO  OPTICAL  THEORY       15 

when  a  ray  of  light  goes  from  air  into  water  or  glass,  the 
ray  is  bent.  Newton  states  that  the  amount  of  bending 
depends  on  the  color  of  the  incident  ray.  His  proof,  as 
usual,  is  by  experiments.  The  first  one  is  as  follows: 
Taking  a  piece  of  paper,  he  draws  a  straight  line 
across  the  middle  and  paints  one  half  of  the  paper  a 
bright  red  and  the  other  a  vivid  blue.  The  paper  is  laid  on  a 
table  before  a  window  and  viewed  through  a  prism  of  glass 
held  with  its  edges  horizontal.  If  the  wedge-shaped  part 
of  the  prism  is  held  upwards,  the  paper  appears  to  be 
lifted  upwards;  but  the  two  halves  are  not  lifted  equally, 
the  blue  being  raised  much  more  than  the  red.  He  con- 
cludes that  blue  light  is  more  refrangible  than  red,  and  by 
varying  the  colors  it  is  easy  to  extend  the  observations 
so  as  to  convince  yourself  that  color  and  refrangibility 
are  intimately  related.  Mr.  Farwell  will  show  you  this, 
with  the  modifications  required  by  the  facts  that  he  is 
working  at  night,  while  Newton  used  sunlight,  and  his 
experiment  must  be  seen  by  a  large  audience  and  not  by 
a  single  observer.  The  second  proposition  of  Newton  is 
that  "The  Light  of  the  Sun  consists  of  rays  differently 
refrangible."  The  proof  by  experiment  was  made  by  dark- 
ening a  room  and  making  a  small  circular  hole  in  the  window 
shutter,  through  which  the  light  could  stream.  This  light, 
falling  on  some  white  paper  on  the  opposite  wall,  produced 
a  light  circular  spot  quite  free  from  color.  He  then  inter- 
posed a  glass  prism  in  the  path  of  the  sunlight,  and  looking 
at  the  paper  on  the  wall,  found,  instead  of  a  circular  color- 
less spot,  a  brilliant  display  of  color  —  what  he  called  a 
spectrum  —  no  longer  round,  but  about  five  times  longer 
than  it  was  broad.  The  fact  that  it  was  not  round  proved 
the  falsity  of  the  current  rules  of  "Vulgar  Opticks,"  as  he 


16  LIGHT 

called  them.  The  arrangement  of  the  colors  in  the  spectrum 
showed  a  difference  of  refrangibility  in  agreement  with  his 
first  proposition;  whilst  the  presence  of  so  many  colors 
indicated  what  a  highly  complex  mixture  sunlight  really  is. 
Mr.  Farwell  will  repeat  the  experiment. 

This  proposition  of  Newton,  which  sets  out  the  composite 
character  of  sunlight,  is  his  most  important  one.  If  you 
really  grasp  it,  you  are  on  the  way  to  understand  most  of  the 
phenomena  of  color.  It  establishes  the  paradox  that  you 
produce  color  by  suppressing  it.  With  all  possible  colors 
mixed,  you  have  colorless  sunlight;  take  out  one  or  more 
of  its  elements,  and  color  is  the  result.  Newton,  of  course, 
realized  the  importance  of  his  proposition,  and  so  he  set 
himself,  even  more  rigorously  than  usual,  to  establish  the 
principle  that  he  thus  enunciates,  "The  Sun's  light  is  an 
heterogeneous  mixture  of  rays,  some  of  which  are  constantly 
more  refrangible  than  others."  He  changes  the  conditions 
of  his  experiments  in  various  ways,  subjects  the  sunlight 
now  to  reflection  and  now  to  refraction,  in  some  cases  from 
natural  bodies,  in  others  from  those  artificially  constructed 
—  in  all  cases  the  results  agree  in  establishing  his  main 
contention.  There  is  no  time  to  describe  these  different 
devices  —  a  single  variant  from  that  already  shown  must 
suffice.  We  have  seen  that  a  ray  of  light  in  water  or  glass 
will  as  a  rule  be  partially  reflected  and  partially  refracted 
when  it  comes  to  the  surface  separating  the  water  or  glass 
from  air.  However,  at  a  certain  angle  of  incidence,  an  angle 
that  is  called  the  critical  angle,  there  will  be  no  refraction, 
and  the  light  will  be  totally  reflected.  Now  Newton  saw 
that  if  different  colored  rays  were  differently  refrangible,  the 
critical  angle  would  be  different  for  each,  and  consequently 
that  if  sunlight  were  composite,  the  phenomenon  of  total 


EARLY  CONTRIBUTIONS  TO  OPTICAL  THEORY       17 

reflection  would  occur  at  different  incidences  for  the 
different  constituents.  To  test  this,  he  took  two  similar 
right-angled  prisms  of  glass  and  held  them  together,  but 
not  quite  in  optical  contact,  so  that  their  cross-section 
formed  a  square.  Under  most  circumstances  the  light 
from  the  sun  falling  perpendicularly  on  such  an  arrange- 
ment would  pass  through  without  change.  Owing,  however, 
to  the  film  of  air  separating  the  two  prisms,  the  angle  of 
incidence  at  this  separating  surface  might  lie,  for  any  color, 
within  the  range  of  total  reflection.  Such  a  color  could 
not  get  through  the  double  prism,  being  totally  reflected  at 
the  common  boundary  of  the  two  prisms.  Thus,  in  the 
beam  'that  emerged,  some  of  the  color  would  be  suppressed, 
and  the  light  would  no  longer  be  white  like  sunlight.  To 
test  its  exact  character,  the  emergent  beam  had  to  be  ana- 
lyzed, and  the  simplest  instrument  for  this  purpose  is  a 
prism  which  separates  the  different  constituents  by  re- 
fracting them  all  differently.  Newton  therefore  placed  a 
prism  behind  his  double  prism,  and  watched  what  happened 
as  the  latter  was  slowly  turned  round  so  as  to  change  the 
angle  of  incidence  on  the  air-space  between  the  two  right- 
angled  prisms.  He  found  that  just  when  the  film  of  air 
met  the  rays  from  the  sun  at  the  critical  angle  for  blue,  the  • 
blue  disappeared  from  the  spectrum  produced  by  his  last 
prism,  and  that  as  the  revolution  was  continued,  all  the 
colors  disappeared  in  succession,  as  the  critical  angle  for 
each  was  reached.  This  I  shall  now  ask  Mr.  Farwell  to 
show  you.  The  arrangement  of  the  apparatus  is  indicated 
in  Fig.  2. 

P1  and  P2  are  the  right-angled  prisms  referred  to.  A 
strip  of  tissue  paper  keeps  them  from  actual  contact,  and 
they  are  held  together  by  an  elastic  band.  The  light  from 


18  LIGHT 

the  electric  lantern  is  focussed  so  as  to  fall  as  a  parallel 
beam  A  B  on  the  layer  of  air  between  the  prisms,  and  if  it 
fall  at  the  right  angle,  the  corresponding  ray  will  be  totally 
reflected  along  BC,  and  so  will  not  enter  the  second  prism, 
P2.  L  is  merely  a  focussing  lens,  P3  is  the  analyzing  prism, 
and  $!$a  the  screen  on  which  the  phenomena  are  observed. 


Fia.  2 

Thus  far  I  have  dealt  with  only  two  of  Newton's  propo- 
sitions. Of  the  many  others  that  he  lays  down  I  can 
refer  to  but  a  few.  Proposition  V:  "Homogeneal  light 
is  refracted  regularly  without  any  dilatation,  splitting,  or 
scattering  of  the  rays."  We  have  seen  that  when  a  beam 
of  sunlight  traverses  a  prism,  its  different  constituents  are 
differently  refracted,  so  that,  instead  of  a  narrow,  colorless 
band,  we  see  a  broad  one  brilliantly  colored,  and  instead 
of  a  white,  circular  spot  representing  the  sun,  we  have  a  long- 
drawn-out  image  with  all  the  colors  of  the  rainbow.  The 
"explanation"  of  this  phenomenon  current  in  Newton's  day 
was  that  the  prism  had  the  power  of  shattering  the  rays, 
an  " explanation"  typical  of  medieval  science,  which  was 
generally  satisfied  with  a  mere  name.  Newton  sounded 
the  death-knell  of  this  theory  by  showing  that  if  the  light 
employed  were  pure, — "  homogeneal ' '  was  his  phrase, — or  if 


OF   THt  A 

UNIVERSITY  ] 

OF  fl 


IBUTIONS  TO  OPTICAL  THEORY 


it  were  red,  or  green,  or  blue,  and  not  a  mixture  of  different 
colors,  then  there  was  none  of  this  spreading  out  of  an 
image,  or  dispersion,  as  we  call  it,  so  that  the  prism  could 
not  be  endowed  with  any  mystic  power  of  shattering  a  ray. 
His  method  of  proving  this  was  as  follows :  He  allowed  a 
ray  of  sunlight  to  stream  into  a  darkened  room.  This  he 


FIG.  3 


intercepted  with  a  prism,  and  so  produced  a  spectrum  with 
all  the  colors  on  a  wooden  screen  behind  the  prism.  This 
screen  was  pierced  with  a  hole  that  allowed  light  to  stream 
through  and  fall  on  a  parallel  screen  behind  it.  The  second 
screen  also  contained  a  hole,  and  by  turning  the  prism  round, 
Newton  could  sift  out  light  from  any  part  of  the  spectrum, 
and  arrange  that  the  light  going  through  the  two  holes 
in  the  screens  should  be  approximately  homogeneous.  He 
then  allowed  this  homogeneous  light  to  pass  through  a 
prism  and  make  an  image  on  a  screen  behind  it.  He 
found  that  there  was  no  appreciable  spreading  out  or 
dispersion  of  the  homogeneous  beam.  Mr.  Farwell  will 
show  this  to  you,  and  Fig.  3  will  serve  to  give  you  a  picture 
of  the  arrangement  of  Newton's  apparatus. 

Another  experiment  devised  to  serve  the  same  end,  and 
one  that  you  can  very  easily  try  for  yourselves,  is  thus 


20  LIGHT 

described  by  Newton:  "In  the  homogeneal  light  I  placed 
flies,  and  such  like  minute  objects,  and  viewing  them 
through  a  prism,  I  saw  their  parts  as  distinctly  defined 
as  if  I  had  viewed  them  with  the  naked  eye.  The  same 
objects  placed  in  the  sun's  unrefracted  heterogeneal  light, 
which  was  white,  I  viewed  also  through  a  prism,  and  saw 
them  most  confusedly  defined,  so  that  I  could  not  dis- 
tinguish their  smaller  parts  from  one  another." 

In  the  second  part  of  the  first  book  of  "Opticks,"  his 
second  proposition  is  as  follows:  "All  homogeneal  light  has 
its  own  proper  color,  answering  to  its  degree  of  refrangi- 
bility,  and  that  color  cannot  be  changed  by  reflection  and 
refraction."  He  proved  by  experiment  that  "  if  any  part  of 
red  light  was  refracted,  it  remained  totally  of  the  same  red 
color  as  before.  No  orange,  no  yellow,  no  green  or  blue,  no 
other  new  color,  was  produced  by  refraction."  And  as  these 
colors  were  not  changeable  by  refraction,  so  neither  were 
they  by  reflection.  For  all  white,  gray,  red,  yellow,  green, 
blue,  or  violet  bodies,  such  as  paper,  ashes,  red  lead,  indigo, 
gold,  silver,  copper,  grass,  violets,  peacocks'  feathers  and 
such  like,  in  red  homogeneal  light  appear  totally  red,  in 
blue  light  totally  blue,  in  green  light  totally  green,  and  so 
of  other  colors.  "From  all  which,"  he  concludes,  "it  is 
manifest  that  if  the  sun's  light  consisted  of  but  one  sort  of 
rays,  there  would  be  but  one  color  in  the  whole  world,  nor 
would  it  be  possible  to  produce  any  new  color  by  reflections 
and  refractions,  and  by  consequence  that  the  variety  of 
colors  depends  upon  the  composition  of  light." 

Time  will  not  permit  me  to  do  more  than  mention  two 
other  important  propositions  of  this  book.  Proposition 
IV:  "Colors  may  be  produced  by  composition  that  shall  be 
like  to  the  colors  of  homogeneal  light  as  to  the  appearance 


EARLY  CONTRIBUTIONS  TO  OPTICAL  THEORY       21 

of  color,  but  not  as  to  its  immutability. "  Proposition  V: 
"  Whiteness  and  all  gray  colors  between  white  and  black 
may  be  compounded  of  colors,  and  the  whiteness  of  the 
sun's  light  is  compounded  of  all  the  primary  colors  mixed 
in  a  due  proportion." 

Having  unlocked  these  secrets  of  Nature,  he  applies  the 
principles  thus  established  to  explain  the  colors  made  by 
prisms,  the  colors  of  the  rainbow,  and  the  permanent  colors 
of  natural  bodies.  And  he  shows  generally  that  "if  the 
reason  of  any  color  whatever  be  required,  we  have  nothing 
else  to  do  than  consider  how  the  rays  in  the  sun's  light 
have,  by  reflections  or  refractions,  or  other  causes,  been 
parted  from  one  another  or  mixed  together." 

Unless  you  know  something  of  modern  physics,  you  will 
not  realize  the  full  significance  of  Newton's  conclusions, 
but  I  hope  you  will  see  that,  having  regard  to  all  that  had 
gone  before,  they  were  epoch-making.  By  the  aid  of  so 
cheap  an  instrument  as  a  prism,  but  with  a  priceless  mind, 
Newton  revealed  the  true  nature  of  color.  Those  of  you 
who  have  visited  the  English  University  of  Cambridge, 
have  probably  been  in  the  Ante-Chapel  of  Trinity  College, 
and  if  you  had  any  knowledge  of  science,  you  must  have 
looked  with  interest,  if  not  with  admiration,  on  a  marble 
statue  of  Newton  standing  pensively  with  a  prism  in  his 
hand.  Long  after  Newton's  day  there  came  as  an  under- 
graduate to  the  same  old  university  the  poet  Wordsworth, 
and  he  tells  us  how,  looking  from  his  rooms  in  a  neighboring 
college,  he  could  behold — 

"  The  antechapel  where  the  statue  stood 
Of  Newton  with  his  prism  and  silent  face, 
The  marble  index  of  a  mind  forever 
Voyaging  through  strange  seas  of  Thought,  alone." 


22  LIGHT 

What  epoch-making  voyages  were  his !  The  one  that 
we  have  dwelt  upon  to-night  would  have  been  enough  to 
make  the  reputations  of  a  score  of  men,  but  as  you  are 
doubtless  aware,  it  is  one  of  the  smallest  of  his  achieve- 
ments. His  contributions  to  mechanics,  celestial  and 
terrestrial,  and  his  introduction  of  the  greatest  engine  of 
advancement  in  scientific  investigation  (the  calculus)  far 
outweigh  in  most  men's  minds  what  he  did  for  optics. 
We  need  not  attempt  to  estimate  the  relative  values  of  these 
various  products  of  his  genius.  It  is  enough  to  recognize 
him,  as  does  the  whole  scientific  world,  as  the  greatest  man 
of  science  that  has  yet  appeared.  The  impression  that  he 
makes  on  the  minds  of  all  who  have  the  capacity  to  under- 
stand him  is  of  a  being  almost  superhuman.  You  feel  that 
you  are  in  the  presence  of  no  ordinary  master.  All  seems  so 
great,  and  yet  done  so  simply  and  without  apparent  effort. 
How  came  these  mighty  powers  to  such  a  man  ?  Is  genius 
hereditary,  and  was  Newton's  thus  acquired?  His  fore- 
bears were  commonplace  enough,  and  there  was  none  of 
eminence  within  the  immediate  circle  of  his  relatives,  so 
that  he  seems  a  sport  of  Nature.  What  natural  advantages 
did  he  have  ?  Was  he  born  rich  as  the  world  counts  riches, 
or  with  the  greater  riches  of  a  fine  physique  ?  His  father 
was  a  mere  yeoman  and,  at  his  birth,  his  mother  a  poor 
widow.  He  was  a  sickly  infant,  not  expected  to  live  for  a 
week.  What  of  his  education?  He  went  to  an  obscure 
school  at  Grantham,  where  I  am  sure  they  knew  little  of 
what  are  now  the  most  approved  methods  of  pedagogy, 
and  afterwards  to  the  University  of  Cambridge,  where  they 
cared  less.  Nature  rarely  seems  to  trouble  much  about  the 
education  of  her  favorite  children,  and  after  all  that  you 
can  say,  the  wind  of  genius  blows  where  it  listeth. 


EARLY  CONTRIBUTIONS  TO  OPTICAL  THEORY       23 

Finally,  what  of  his  character  ?  It  comes  as  a  shock  to 
find  a  grave  moral  weakness  in  a  great  man.  One  thinks 
of  Bacon  and  the  cutting  description  of  him,  doubtless 
somewhat  exaggerated,  as  "the  greatest,  wisest,  meanest 
of  mankind."  Fortunately,  amongst  the  leaders  of  modern 
physics,  there  has  been  no  such  unhappy  combination. 
To  speak  only  of  the  dead,  such  men  as  Faraday,  Maxwell, 
Helmholtz,  Fitzgerald,  and  Stokes  were  men  whose  moral 
dignity  everywhere  commanded  respect.  And  I  am  glad 
to  say  that  this  was  true  of  Newton  in  a  preeminent  degree. 
His  was  a  nature  of  unusual  dignity  and  calm,  absolutely 
free  from  the  petty  ambitions  of  lesser  minds,  and  modest 
to  a  degree.  As  an  old  man,  worshiped  by  the  intellect  of 
Europe  as  the  greatest  of  his  race,  these  were  his  words : 
"I  know  not  what  the  world  will  think  of  my  labors, 
but  to  myself  it  seems  that  I  have  been  but  as  a  child  play- 
ing on  the  sea-shore,  now  finding  some  pebble  rather  more 
polished,  and  now  some  shell  rather  more  agreeably  varie- 
gated than  another,  while  the  immense  ocean  of  truth  ex- 
tended itself  unexplored  before  me." 

Just  one  word  more.  How  often,  when  all  else  about  a 
man  is  satisfactory,  his  mere  look  disappoints!  On  the 
screen  is  thrown  a  portrait  of  Newton,  and  in  contempla- 
tion of  that  beautiful  face  perhaps  I  may  appropriately 
leave  you. 


II 


COLOR   VISION    AND    COLOR    PHOTOGRAPHY 

As  the  arrangement  of  this  course  is  not  entirely  hap- 
hazard, it  is  of  some  importance  that  at  each  lecture  you 
should  recall  the  main  results  reached  in  what  has  gone 
before.  Apart  from  the  simple  laws  of  reflection  and  re- 
fraction, our  chief  concern  in  the  last  lecture  was  the 
phenomenon  of  color,  and  the  most  important  conclusions 
were  two :  first,  that  there  is  an  intimate  relation  between 
color  and  ref rangibility ;  and  second,  that  sunlight  is  not 
a  simple  thing,  but  a  compound  of  numberless  constituents. 
I  would  have  you  remember  that  all  the  results  were 
based  on  experiments  that  you  actually  saw  performed. 
Of  course  the  facts  are  one  thing,  and  the  language  in  which 
you  choose  to  describe  them  is  another.  Science  has  her 
own  language,  unfortunately  a  highly  technical  one  in  these 
latter  days.  I  remember  the  regret  expressed  by  a  distin- 
guished scholar  of  my  own  university  for  the  good  old 
days,  when  men  of  science  could  express  themselves  in  a 
pleasing  Latinity  that  every  scholar  could  understand. 
The  change  is,  for  many  reasons,  to  be  deplored.  I  do  not 
refer  merely  to  the  obvious  loss  that  comes  from  the  aban- 
donment of  a  universal  language,  but  rather  to  the  evils 
that  ensue  from  the  splitting  up  of  scientific  language  by 
repeated  specialization,  so  that  a  chemist  no  longer  under- 
stands a  physicist,  and  neither  has  anything  but  the  faintest 
conception  of  what  a  botanist  is  talking  about. 

24 


COLOR  VISION  AND  COLOR  PHOTOGRAPHY  25 

For  good  or  evil,  a  physicist  likes  to  make  use  of  me- 
chanical terms,  and  feels  that,  when  he  does  so,  he  knows 
his  own  language  and  can  express  himself  with  precision. 
How,  then,  is  he  to  describe  the  phenomena  of  light? 
He  does  it  with  the  aid  of  terms  that  naturally  suggest 
themselves  when  dealing  with  the  familiar  experience  of 
wave-motion.  Waves  in  some  form  or  another  we  all  know 
well,  whether  in  air  or  water  or  the  solid  earth.  When  I 
speak,  a  wave  of  sound  spreads  into  the  room,  and  at  every 
point  where  my  voice  is  heard  there  is  a  to-and-fro  motion 
of  the  air,  a  periodic  disturbance,  as  it  is  called,  that  con- 
stitutes the  essential  feature  of  a  wave-motion.  At  sea 
the  wind  disturbs  the  water  and  sets  up  a  to-and-fro  mo- 
tion that  rocks  you  and  the  ship  in  which  you  lie,  gently 
or  otherwise,  in  the  cradle  of  the  deep.  Some  great  up- 
heaval in  the  earth  itself  originates  a  to-and-fro  motion 
which  spreads  as  an  earthquake  wave  around  the  globe 
with  havoc  in  its  trail.  In  all  these  cases  you  have  a  to-and- 
fro  motion  in  a  medium  —  the  media  being  air,  water, 
and  the  earth.  According  to  modern  physics,  light  is  due 
to  just  such  a  to-and-fro  motion — a  wave,  if  you  prefer  the 
term  —  in  a  medium  that  we  call  the  ether.  This  ether  is  an 
abstraction;  that  is,  it  is  conceived  of  by  abstracting  or 
picking  out  certain  qualities  of  air  and  earth  and  water, 
and  refusing  to  abstract  some  others.  Why  should  we 
perform  this  curious  feat?  Because  it  helps  us  to  do 
wonders,  to  coordinate  with  simplicity  and  ease  countless 
optical  phenomena  that  no  mind  could  otherwise  grasp 
and  no  memory  retain;  while,  without  it,  all  seems 
chaos. 

In  the  to-and-fro  disturbance  that  we  call  wave-motion 
there  are  two  elements  of  special  importance :  the  magni- 


26  LIGHT 

tude  of  the  disturbance,  —  amplitude  is  the  technical  term,  — 
and  the  frequency. 

Watch  a  cork  floating  on  the  smooth  surface  of  the 
Hudson  River,  and  then  observe  it  bobbing  up  and  down 
as  a  wave  advances  over  it.  The  greatest  height  it  rises 
is  the  amplitude,  the  number  of  times  it  moves  upwards 
in  a  second  is  the  frequency.  On  these  two  elements, 
amplitude  and  frequency,  more  than  on  anything  else, 
will  depend  the  damage  that  the  wave  does  if  it  strikes  a 
movable  object.  If  the  wave  be  very  high,  it  will  have  great 
capacity  for  work,  useful  or  destructive ;  under  such  cir- 
cumstances, it  is  said  to  be  of  great  intensity.  But  what 
it  effects  will  also  depend  very  largely  on  the  frequency. 
I  shall  have  to  emphasize  this  so  much  in  the  next  lecture 
that  now  I  need  do  no  more  than  state  the  fact. 

I  have  said  that,  according  to  modern  theories,  light  is 
to  be  regarded  as  due  to  waves  in  the  ether.  The  effect 
of  these,  as  of  any  other  waves,  will  depend  on  what  they 
strike.  Light,  of  course,  may  shine  on  a  stone,  but  the 
stone  will  certainly  not  see  light.  Hence,  if  we  are  to  under- 
stand the  phenomena  of  light,  we  must  know  something  of 
the  mechanism,  the  eye,  that  receives  the  impress  of  the 
ether  waves.  According  to  our  theory,  the  waves  in  the 
ether  beat  upon  the  eye  in  much  the  same  way  that  waves 
in  the  sea  dash  themselves  on  a  rock-bound  coast.  The 
analogy,  however,  would  be  closer  and  more  instructive 
if  we  took  the  case  of  waves  dashing  on  something  that  is 
itself  movable.  Think  of  the  waves  striking  a  ship  at 
sea ;  their  effect  depends  mainly  on  their  height  and  on  their 
frequency.  So  it  is  with  waves  of  light  beating  against  the 
eye.  Great  height  corresponds  to  great  intensity,  a  brilliant 
light;  frequency  is  the  clue  to  color.  If  the  ether  waves 


COLOR  VISION  AND  COLOR  PHOTOGRAPHY  27 

strike  on  a  normal  eye  450  million  million  times  per  second, 
then  no  matter  what  their  intensity,  they  produce  the  sensa- 
tion of  red;  if  550  million  million  times  per  second,  they 
produce  the  sensation  of  green;  if  600  million  million  times 
per  second,  the  sensation  of  blue.  If  the  eye  be  abnormal, 
the  color  sensation  may  be  quite  different. 

At  this  stage  the  interesting  and  important  question  arises : 
Can  the  sensation  of  blue  (or  similarly  of  any  other  color) 
be  produced  in  any  other  way  than  by  the  regular  impact 
of  ether  waves  striking  the  eye,  and  setting  up  periodic 
disturbances  therein,  at  the  rate  of  600  million  million  per 
second  ?  The  answer  is  that  it  can.  Newton  knew  this, 
and  stated  it  in  one  of  his  propositions  quoted  in  the  last 
lecture,  and  long  before  Newton's  time  the  artists  had  learned 
it  from  experience.  To  paint,  it  is  not  necessary  to  have 
every  color  on  your  palette,  for  although  it  may  be  con- 
venient to  have  quite  a  number,  you  can  produce  almost 
any  effect  by  the  proper  mixture  of  a  few.  By  pondering 
over  these  facts,  a  theory  of  primary  colors  was  evolved, 
a  primary  color  being  one  that  cannot  be  formed  by  the 
mixture  of  any  other  colors.  The  artists,  working  with 
impure  colors,  decided  that  the  primary  colors  were 
three  —  red,  yellow,  and  blue ;  had  they  been  able  to  effect 
a  mixture  of  pure  colors,  they  would  have  fixed  on  red 
and  green  and  violet.  This  important  fact  is  sometimes 
enunciated  in  an  algebraic  form,  what  is  called  a  color 
equation,  and  may  be  thus  expressed:  — 

Any  color  =  aR  +  bG  4-  cV, 

provided  the  coefficients  a,  b,  c  be  properly  chosen. 

It  may  interest  and  amuse  you  to  test  this  statement 
for  yourselves.  Nothing  but  the  simplest  apparatus  is 


28  LIGHT 

required,  —  a  common  top,  a  stiff  piece  of  paper,  and  pig- 
ments that  give  the  three  colors,  red,  green,  and  violet. 
Cut  out  a  circular  disk  from  your  paper  and  divide  it  into 
sectors  by  drawing  lines  from  the  center.  Paint  three 
sectors  with  the  three  different  colors,  place  the  disk  on 
the  top,  and  spin  it.  As  it  spins,  you  will  perceive  a  definite 
color  due  to  the  mixture  of  the  three  in  the  proportions 
that  you  have  chosen,  and  by  varying  those  proportions 
(i.e.  by  altering  the  size  of  the  sectors),  you  will  learn  to 
produce  any  color  that  you  may  desire. 

Before  proceeding  farther,  I  wish  to  impress  on  you  the 
fact  that  I  am  not  now  presenting  any  theory,  but  merely 
stating  certain  facts  of  observation.  All  the  colors  that 
we  know  can  be  produced  by  suitable  mixtures  of  these 
three,  Red,  Green,  and  Violet.  This  is  the  great,  though 
certainly  not  the  only,  fact  that  any  theory  of  color  vision 
has  to  account  for.  These  theories  deal  with  the  mechanism 
of  the  eye,  and  their  object  is  to  suggest  a  mode  of  working 
that  will  fit  in  with  all  the  facts.  Of  various  rival  theo- 
ries, only  two  are  worth  considering  to-night.  The  first  was 
clearly  stated  by  Young,  and  afterwards  developed  by 
Maxwell  and  Helmholtz,  all  men  of  the  first  rank  as  physi- 
cists, so  that  their  ideas  naturally  commend  themselves  to 
men  trained  in  physical  science.  The  other  is  more  modern 
in  its  origin ;  it  was  suggested  by  Hering,  and  being  couched 
in  physiological  language,  finds  more  favor  with  the  physi- 
ologists than  with  the  physicists. 

As  far  as  the  perception  of  color  is  concerned,  it  is  agreed 
that  the  most  important  part  of  the  eye  is  that  inner  wall, 
the  retina,  which  is  connected  with  the  brain  by  the  optic 
nerve.  Close  to  this  wall  there  is  arranged  a  curious  layer 
of  what  are  known  as  rods  and  cones,  some  three  million 


COLOR  VISION  AND  COLOR  PHOTOGRAPHY 


29 


of  the  latter  in  an  average  eye.  It  is  suggested  that  these 
rods  and  cones  are  the  chief  part  of  the  mechanism  which, 
when  disturbed  by  an  incoming  ether  wave,  transmits  the 
sensation  of  color  to  the  brain.  According  to  the  Young- 
Helmholtz  theory,  these  little  cones  can  be  separated  into 
three  classes,  Red,  Green  and  Violet,  according  to  the  sensa- 


A        D  yC         D 


H 


FIG.  4 


tion  that  they  are  capable  of  transmitting,  or  more  accurately 
according  to  the  color  to  which  they  are  most  sensitive. 
If,  for  convenience,  we  call  them  the  R,  G,  and  V  cones, 
the  V  cone  is  most  sensitive  to  violet,  the  G  to  green,  and  the 
R  to  red.  It  must  be  understood,  however,  that  each  cone 
is  more  or  less  sensitive  throughout  a  considerable  range  of 
frequency.  Perhaps  it  will  tend  to  clearness  if  we  repre- 
sent the  state  of  affairs  on  a  diagram. 

The  three  curves  in  the  figure  show  the  sensitiveness  of  the 
R,  G,  and  V  cones  when  they  are  stimulated  by  waves  of  differ- 
ent frequencies.  The  frequencies  are  indicated  by  distances 
measured  horizontally  across  the  page  and  also  by  the 
numbers  set  out  below  the  line  AH.  These  are  the  number 
of  million  million  vibrations  in  a  single  second,  so  that 
395  at  A  indicates  that,  corresponding  to  this  point  in  the 


30  LIGHT 

diagram,  the  incoming  wave  is  oscillating  to  and  fro  395 
million  million  times  each  second. 

The  distances  measured  at  right  angles  to  the  line  AH 
indicate  the  corresponding  sensitiveness  of  the  three  differ- 
ent cones,  the  scale  being  chosen  so  that  when  the  three 
cones  are  equally  stimulated,  a  sensation  of  white  is  pro- 
duced. One  very  important  fact  indicated  by  this  diagram 
is  that  the  range  of  frequencies  that  stimulate  the  eye 
at  all  is  finite.  In  the  figure  it  extends  from  B  to  a,  i.e. 
from  437  to  775  million  million  vibrations  per  second. 
There  are  many  means  of  setting  up  vibrations  having 
frequencies  outside  these  limits,  but  they  produce  no  sen- 
sation of  light  in  a  normal  eye.  However,  the  special 
purpose  of  the  diagram  is  to  indicate  the  relative  sensi- 
tiveness of  the  different  cones  to  a  stimulus  of  given  fre- 
quency. The  V  cones  are  sensitive  only  in  the  range  afi, 
that  is,  for  frequencies  lying  between  775  and  550  million 
million,  and  are  most  sensitive  when  the  frequency  is  about 
650  million  million.  The  G  cones  are  sensitive  from  G 
to  7,  when  the  frequencies  lie  between  696  and  450  million 
million,  and  are  most  affected  when  the  frequency  is  about 
550  million  million.  Lastly,  the  R  cones  are  sensitive  in 
the  range  H  to  B,  where  the  frequency  varies  from  755  to 
437  million  million,  and  they  are  most  violently  affected 
when  the  incoming  wave  tosses  the  ether  to  and  fro  about 
520  million  million  times  per  second.  Just  one  more  point 
before  we  dismiss  this  diagram:  the  color  anywhere  in 
the  spectrum  may  be  regarded  as  made  up  of  not  more  than 
two  sensations,  with  a  dash  of  white.  You  will  see  from 
the  figure  that  it  is  only  in  the  region  GyS  that  more  than 
two  of  the  cones  are  stimulated  simultaneously.  At  any 
point  of  this  region,  such  as  p,  if  we  draw  the  line  pqrs,  the 


COLOR  VISION  AND  COLOR  PHOTOGRAPHY  3t 

parts  qr  and  qs  show  that  the  R  and  G  cones  are  stimulated 
so  as  to  give  the  sensation  of  red  and  green,  while  the  part 
pq  shows  that,  to  this  extent,  all  three,  R,  G,  and  V,  are 
equally  stimulated,  and  this  equal  stimulation  corresponds 
to  the  sensation  of  white. 

So  far  we  have  dealt  only  with  the  Young-Helmholtz 
theory  of  color  vision.  The  rival  theory  of  Hering  is 
based  on  the  observation  that  in  most  of  the  changes  that 
take  place  in  living  subjects,  two  main  phases  present  them- 
selves. In  the  first,  we  have  a  constructive  phase,  when  an 
organism  appears  to  be  built  up  out  of  lower  forms,  while 
in  the  second  a  destructive  process  sets  in  that  decomposes 
the  organism  into  lower  elements.  Hering  supposes  that 
there  exists  in  the  retina  a  visual  substance  that  has  three 
different  constituents.  The  first  we  may  call  the  Red- 
green,  the  second  the  Yellow-blue,  and  the  third  the  White- 
black  constituent.  When  an  ether  wave  falls  on  the  Red- 
green  substance,  it  may  not  affect  it  at  all ;  but  if  it  has  the 
right  frequency,  it  may  set  in  motion  the  constructive  ma- 
chinery, and  so  give  the  sensation  green;  or,  on  the 
other  hand,  it  may  start  the  destructive  process,  and  red  will 
be  seen.  (Some  find  support  for  this  theory  from  their  ex- 
perience that  red  is  a  tiring  color  to  look  at  long,  while 
green  is  not.)  The  same  sort  of  thing  may  happen  to  the 
other  constituents;  for  example,  to  the  Yellow-blue  one. 
A  certain  frequency  may  set  up  the  process  of  destruction, 
and  we  have  yellow ;  whereas  a  differently  timed  stimulus 
induces  construction,  and  a  sensation  of  blue  is  the  result. 

We  shall  not  have  time  this  evening  to  enter  into  a  com- 
parison of  the  merits  and  demerits  of  these  rival  theories. 
They  must  be  tested,  of  course,  by  their  correspondence 
with  the  facts  of  experience.  As  far  as  the  few  facts  hitherto 


32  LIGHT 

marshalled  are  concerned,  either  theory  would  do,  as  in  fact 
would  almost  any  other  that  suggested  a  mechanism  sensitive 
to  three  or  four  different  kinds  of  impressions.  No  such 
theory  explains  anything  as  far  as  color  is  concerned. 
The  facts  as  to  color  are  known;  the  object  of  the  theory 
is  to  go  from  the  known  facts  to  the  unknown  mechanism 
of  the  eye  that  perceives.  But  although  we  have  no  time 
to  discuss  these  theories  further,  we  may  perhaps  just  in- 
dicate the  direction  in  which  we  must  go  if  a  decision  as  to 
their  relative  merits  is  to  be  reached.  We  must,  of  course, 
look  at  all  the  facts,  but  we  should  pay  special  attention 
to  those  that  are  likely  to  tell  us  most  about  the  mechanism 
of  the  eye.  You  will  have  observed  that  it  is  generally 
when  a  machine  goes  wrong  that  you  begin  really  to  under- 
stand how  it  works  or  should  work.  When  all  is  running 
smoothly,  you  sit  comfortably  in  your  automobile  and 
care  little  how  it  works.  There  is  nothing  to  think  about 
except,  perhaps,  to  decide  by  the  mere  turn  of  a  handle 
whether  a  humble  pedestrian  is  to  be  your  victim  or  not. 
Let,  however,  something  go  wrong  that  brings  you  to  your 
proper  position  under  the  machine ;  then  you  begin  to  really 
know  its  mechanism.  So  it  is  with  most  machines ;  the  study 
of  their  defects  and  shortcomings  is  the  surest  road  to  a 
mastery  of  their  working.  Now  the  eye  is  not  a  perfect 
machine,  and  one  of  its  defects,  and  by  no  means  an  un- 
common one,  produces  color  blindness.  Some  see  no  red, 
others  no  green,  and  a  few  no  violet,  whilst  now  and  then 
a  person  is  found  who  sees  neither  red  nos  violet.  It  is 
by  the  careful  study  of  such  abnormalities  that  we  may 
best  hope  to  test  the  merits  and  defects  of  any  theory 
of  color  vision. 
And  now,  as  time  is  short,  I  must  pass  somewhat  abruptly 


COLOR  VISION  AND  COLOR  PHOTOGRAPHY         33 

to  consider  that  other  subject  announced  for  discussion 
at  this  lecture  —  the  subject  of  color  photography.  You 
will  see  at  a  glance  that  the  two  subjects  of  color  vision 
and  photography  are  not  quite  strangers  to  each  other.  It 
is  obvious  that  the  methods  of  giving  to  the  eye  the  impres- 
sion of  the  colors  of  a  landscape  must  depend  in  some 
way,  intimate  or  remote,  on  the  mechanism  of  vision.  At 
the  same  time  it  soon  appears  that  we  can  progress  with 
color  photography  without  coming  to  a  complete  under- 
standing as  to  the  true  theory  of  color  vision.  Whether 
we  accept  the  Young-Helmholtz  theory,  or  lean  towards 
the  rival  one  of  Hering,  or  prefer  some  modification  of 
either,  will  not  much  affect  our  grasp  of  the  principles  of 
color  photography  or  our  skill  in  its  art.  To  understand 
these  principles,  the  one  thing  needful  is  the  full  realization 
of  the  fact,  already  emphasized  as  crucial,  that  any  color 
can  be  produced  by  a  proper  combination  of  a  finite  number 
of  colors,  for  example,  by  a  mixture  of  pure  red  and  green 
and  violet. 

It  is  sometimes  thought  that  color  photography  is  a 
thing  of  yesterday ;  in  reality  it  has  occupied  men's  minds 
seriously  for  about  seventy  years.  To  trace  the  develop- 
ment throughout  that  period  and  to  indicate  the  means 
adopted  to  overcome  the  countless  difficulties  that  have 
arisen,  would  be  a  fascinating  study  of  ingenuity  and  pa- 
tience. For  this,  however,  we  have  no  time  this  evening, 
but  must  hasten  to  a  brief  description  of  a  few  of  the  more 
recent  methods.  The  problem  has  been  attacked  in  two 
totally  distinct  ways,  which  it  is  usual  to  distinguish  by  the 
adjectives  direct  and  indirect.  The  aim  of  the  direct  method 
is  to  prepare  a  surface  that  is  sensitive  to  light  and  that  is 
so  affected  by  the  different  colors  that  it  reflects  blue  if  it 


34  LIGHT 

has  been  touched  by  blue,  red  if  it  has  been  touched  by  red, 
and  so  for  all  the  other  colors.  By  far  the  most  important 
step  in  this  direction  was  taken  in  1891  by  Lippmann, 
although  since  then  his  process  has  been  much  improved 
by  others.  It  would  be  impossible  to  explain  the  process 
intelligibly  without  some  reference  to  the  Principle  of 
Interference,  an  optical  principle  of  great  importance  that 
must  be  dealt  with  in  a  later  lecture.  Perhaps,  then,  it 
will  be  advisable  to  postpone  any  further  reference  to  this 
method  until. the  principle  of  interference  has  been  dis- 
cussed. I  may  say  here,  however,  that  up  to  the  present 
no  direct  process  has  been  so  successful  as  the  indirect,  and 
that  in  this  contest,  as  in  others,  it  has  been  found  that  a 
flank  movement  is  more  effective  than  a  frontal  attack. 

To  those  who  know  in  any  measure  the  immense  debt 
that  modern  science,  and  particularly  the  science  of  light, 
owes  to  Maxwell,  it  is  interesting  to  recall  the  fact  that  it 
was  he  that  found  the  clue  to  the  indirect  method  that  in 
later  days  has  proved  so  effective.  As  long  ago  as  1855, 
in  a  paper  contributed  to  the  Royal  Society  of  Edinburgh, 
he  wrote  as  follows:  "Let  it  be  required  to  ascertain  the 
color  of  a  landscape  by  means  of  impressions  taken  on  a 
preparation  equally  sensitive  to  rays  of  every  color.  Let 
a  plate  of  red  glass  be  placed  before  the  camera,  and  an 
impression  taken.  The  positive  of  this  will  be  transparent 
wherever  the  red  light  has  been  abundant  in  the  landscape, 
and  opaque  where  it  has  been  wanting.  Let  it  now  be  put 
in  a  magic  lantern,  along  with  the  red  glass,  and  a  red  pic- 
ture will  be  thrown  on  the  screen.  Let  this  operation  be 
repeated  with  a  green  and  a  violet  glass,  and  by  means  of 
three  magic  lanterns  let  the  three  images  be  superposed  on 
the  screen.  The  color  of  any  point  on  the  screen  will 


COLOR  VISION  AND  COLOR  PHOTOGRAPHY         35 

depend  on  that  of  the  corresponding  point  of  the  landscape, 
and  by  properly  adjusting  the  intensities  of  the  lights, 
etc.,  a  complete  copy  of  the  landscape,  as  far  as  visible  color 
is  concerned,  will  be  thrown  on  the  screen."  Here  you 
have  a  clear  indication  of  the  path  that  will  lead  to  the 
desired  summit;  but  it  is  one  thing  to  point  out  the  way 
(a  very  useful  thing,  of  course)  and  quite  another  to  actually 
do  the  climbing.  Difficulties  of  all  sorts,  some  expected, 
others  unlooked-for,  may  be  encountered.  Let  us  see 
something  of  the  difficulties  that  have  arisen  in  trying  to 
follow  Maxwell's  directions. 

Before  attempting  this,  it  may  be  well  to  recall  to  your 
minds  the  process  of  ordinary  photography,  now  so  familiar 
to  everybody,  and  to  describe  it  in  the  language  of  the 
modern  theory  of  light.  A  photographic  film  or  plate  is 
coated  with  a  substance,  which,  like  every  ordinary  piece  of 
matter  is,  according  to  the  generally  accepted  theory,  made 
of  molecules  — each  molecule  being  a  group  of  smaller 
parts,  the  atoms.  When  a  wave  of  light  beats  upon  such 
a  plate,  it  shakes  up  the  molecules  more  or  less  violently, 
and  tends  to  shatter  them  to  pieces.  It  does  not  destroy 
them;  but,  if  its  action  be  forceful  enough,  it  so  disturbs 
the  atoms  as  to  alter  their  relative  positions  and  thus  to 
constitute  new  groups  or  molecules.  The  new  molecules 
have  different  chemical  properties  from  the  old,  and  the 
change  is  usually  described  by  saying  that  a  chemical  action 
has  taken  place,  or  that  light  may  affect  things  chemically. 
Whether  any  such  action  takes  place  depends  chiefly  on 
two  things :  the  intensity  and  the  frequency  of  the  wave  of 
light.  A  difficulty  sometimes  arises  in  the  minds  of  thought- 
ful amateurs  when  they  hear  or  read  such  statements 
as  these.  They  emphasize  the  shortness  of  the  exposure 


36  LIGHT 

required  to  affect  a  photographic  plate,  and  ask  how  a  little 
wave  of  light  can  do  so  much  in  one-tenth  or  one-hundredth 
of  a  second.  To  understand  this,  you  must  bear  in  mind 
the  enormously  high  frequencies  of  a  wave  of  light.  The 
frequency  depends  upon  the  color,  but  we  have  seen  that  in 
round  numbers  and  within  the  visible  spectrum  it  lies  between 
400  and  800  million  million.  Imagine  that  you  are  watching 
a  log  floating  in  the  sea,  and  that  it  strikes  against  a  pier  as 
it  rises  and  falls  with  the  waves,  say  once  in  six  seconds  — 
a  not  unusual  state  of  affairs.  What  length  of  time  would 
correspond  to  the  exposure  of  a  photographic  plate  to  violet 
light  for  one-tenth  of  a  second  ?  It  is  a  simple  question  of 
arithmetic. 

800  x  1Q12  vibrations  =  8  x  1013  x  6  seconds 

o  v  ini3  v  a 

= OX1U    xo years  =  2  - 1  X  108  years, 

60  x  60  x  24  x  365  J 

or  more  than  two  million  years.  The  log  might  do  something 
to  the  pier  in  that  time,  and  so  it  is  not  altogether  surprising 
that,  in  an  exactly  corresponding  time,  the  light  does  some- 
thing to  the  photographic  plate. 

Let  us  suppose,  then,  that  light  from  the  various  points  of 
a  human  face  beat  upon  a  photographic  plate  for  one-tenth  of 
a  second.  The  light  from  different  parts  will  have  different 
intensities,  as  there  will  be  gradations  of  light  and  shade. 
The  more  intense  light  will  batter  the  molecules  more 
violently  than  the  feebler  light,  and  so  will  produce  greater 
chemical  action,  which  will  show  itself  by  greater  blackness. 
Thus  the  lighter  the  object  the  blacker  will  be  its  image 
on  the  plate.  In  this  way  is  produced  the  familiar  negative, 
the  gradations  of  light  and  darkness  in  the  face  correspond- 
ing exactly  to  those  of  darkness  and  light  in  the  negative, 


COLOR  VISION  AND  COLOR  PHOTOGRAPHY         37 

and  it  is  by  the  gradation  of  light  and  shade  that  the  whole 
picture  is  presented  to  the  eye.  If  now  we  place  this  nega- 
tive in  front  of  a  paper  that  is  sensitive  to  light,  and  allow 
the  light  to  stream  through  the  negative  on  to  the  paper, 
you  realize  at  once  that  the  blacker  parts  of  the  negative 
will  let  through  less  light  than  the  lighter  parts,  and  thus 
that  the  parts  of  the  paper  underneath  very  dark  portions 
of  the  negative  will  scarcely  be  affected  at  all,  while  those 
below  bright  portions  will  be  battered  and  blackened.  In 
this  manner  is  produced  a  positive,  and  the  gradations  of 
light  and  shade  in  this  will  correspond  to  those  in  the 
original  object,  and  thus  present  a  more  or  less  perfect  like- 
ness. Of  course  some  means  must  be  employed  to  fix  the 
negative  and  the  positive,  so  that  they  will  not  be  sensitive 
to  light  after  exposure.  It  would  be  out  of  place  to  discuss 
such  problems  here ;  I  am  merely  recalling  to  you  the  main 
features  of  what  I  hope  is  familiar  ground.  Now  if  you 
have  had  any  experience,  you  will  realize  that  there  are 
many  places  where  you  may  go  wrong  and  that  to  produce 
a  first-class  photograph  you  must  know  with  precision 
many  things;  e.g.  how  long  to  expose  your  negative, 
under  what  conditions  and  for  what  time  to  develop  it, 
how  best  to  fix  it,  and  so  with  the  positive.  It  is  sometimes 
said  that  in  producing  a  photograph  there  are  only  two 
operations,  making  the  negative  and  the  positive,  but  of 
course  each  of  these  is  complex,  and  if  you  go  wrong  in 
any  one  of  at  least  half  a  dozen  different  operations,  you 
spoil  the  photograph.  With  color  photography,  as  prac- 
tised until  very  recently,  the  difficulty  is  just  this,  that  there 
are  so  many  operations  requiring  precision  and  skill,  and 
consequently  so  many  possibilities  of  marring  the  final 
result. 


38  LIGHT 

The  fundamental  idea  of  most  processes  in  color  pho- 
tography is  to  obtain  different  photographs  of  the  different 
colored  parts  of  the  object  and  superpose  them.  Watch 
a  chromo-lithographer  at  work,  and  you  will  see  him  make 
a  great  many  pictures.  One  represents  the  dark  red  portion 
of  the  object,  another  a  different  shade  of  red,  then  there 
may  be  several  blues,  and  so  on.  When  all  these  are  super- 
posed, we  get  a  picture  more  or  less  like  the  original.  If 
the  color  scheme  is  at  all  complex,  many  separate  pictures 
must  be  made  before  they  can  be  combined,  so  that  if  we 
applied  the  same  principle  to  photography  we  might  need 
20  or  30  different  photographs  to  unite  into  a  single  pic- 
ture. Were  this  the  case,  the  problem  of  color  photography 
would  be  practically  hopeless,  as  each  photograph  involves 
so  many  processes,  each  with  its  pitfalls.  Owing,  however, 
to  the  cardinal  fact  already  emphasized,  that  any  color 
can  be  made  by  a  suitable  mixture  of  a  few,  viz.  Red  and 
Green  and  Violet,  the  process  is  greatly  simplified.  At 
most,  three  separate  photographs  are  needed;  hence  the 
term,  three-color  photography. 

Even  with  this  simplification  the  process  is  difficult  enough. 
Many  are  the  methods  that  have  been  suggested,  but  it 
will  probably  make  for  clearness  if  I  describe  in  outline  a 
single  one,  and  as  far  as  principles  are  concerned,  to  under- 
stand one  is  to  understand  all.  It  is  convenient  to  sepa- 
rate three  different  steps  in  the  process:  (A)  the  analysis 
of  the  complex  colored  light  into  three  constituents  and 
the  production  of  three  corresponding  negatives;  (B)  the 
making  of  three  positives  from  these  negatives;  (C)  the 
recomposition  of  the  three  colored  elements  so  as  to  com- 
pletely represent  the  original  object. 

(A)  The  analysis  is  done  by  means  of  light  filters,  an 


COLOR  VISION  AND  COLOR  PHOTOGRAPHY          39 

arrangement  either  of  colored  liquid  or  of  films  of  colored 
gelatine  interposed  between  the  object  and  the  photo- 
graphic plate.  Thus,  if  a  vessel  containing  red  liquid  be 
placed  before  the  lens,  all  but  the  red  rays  will  be  filtered 
out,  and  only  the  red  part  of  the  picture  will  impress  itself 
on  the  plate.  We  have  now  such  a  variety  of  coloring 
materials  at  our  disposal  that  we  can  get  a  filter  of  almost 
any  color  that  we  want;  but  the  exact  filtering  qualities 
of  any  substance  are  determined  by  other  things  than  mere 
color,  and  these  are  things  that  the  unaided  eye  is  not 
competent  to  detect.  After  many  thousands  of  experi- 
ments, an  immense  amount  of  knowledge  has  been  garnered 
in  this  field.  The  light  that  shines  through  two  liquids 
may  appear  of  exactly  the  same  color  to  the  eye,  but  it 
may  affect  similar  photographic  plates  differently  in  the 
two  cases.  However,  different  plates  are  differently  sensi- 
tive to  the  same  light,  and  it  was  the  discovery  that  plates 
coated  with  different  chemicals  are  differently  affected  by 
the  light,  that  really  made  color  photography  possible. 
By  this  time  we  have  learned  how  to  prepare  a  plate  A, 
that  will  be  sensitive  to  light  that  comes  through  filter  a, 
and  be  little  affected  by  the  light  from  filters  6,  c,  and  d} 
while  plate  B  is  sensitive  to  the  light  that  filters  through  b 
and  is  not  much  influenced  by  the  others,  and  so  for  all  the 
series. 

It  must  be  noted,  however,  that  we  need  to  know  not 
only  that  a  plate  is  sensitive,  but  the  character  of  its  sen- 
sitiveness. How  long  are  you  to  expose  is  an  important 
question  in  ordinary  photography,  and  it  is  peculiarly  so 
in  three-color  work,  for  if  you  make  the  reds  too  deep,  or 
the  greens  too  faint,  you  will  utterly  mar  the  effect.  Hence 
you  must  know  with  some  precision  the  relative  sensitive- 


40  LIGHT 

ness  of  the  different  plates  employed  in  the  process.  Of 
course,  having  obtained  the  negatives,  they  must  be  devel- 
oped and  fixed  as  in  ordinary  photography. 

So  much  for  (A),  the  analysis  of  the  light  and  the  pro- 
duction of  the  negatives.  Now  turn  to  (J5),  the  making  of 
the  three  positives.  Here  the  main  point  to  bear  in  mind 
is  that  an  almost  perfect  agreement  between  the  three 
colored  elements  is  essential.  Color  is  so  delicate  a 
creature  that  the  slightest  discord  will  jar.  Hence  the  sen- 
sitive paper  used  for  obtaining  the  positives  requires 
unusual  care  in  its  production  and  treatment.  The  paper 
must  be  as  nearly  as  possible  inextensible,  and  the  sensitive 
film  of  uniform  thickness.  The  positives  may  then  be 
obtained  from  the  negatives  by  the  ordinary  process,  and 
thus  three  colorless  images  are  formed,  each  made  up  of 
reliefs  in  gelatine.  These  films  are  then  put  into  baths 
that  give  them  respectively  the  three  colors  corresponding 
to  the  original  analysis  by  the  light  filters.  It  should  be 
noted  that  if,  as  in  the  process  we  are  now  describing,  the 
three  pictures  are  not  placed  side  by  side  and  composed 
into  one  by  some  optical  device,  but  are  merely  superposed, 
and  if  further,  as  in  this  process,  pigments  are  used  to  give 
the  colors  in  the  positives,  then  the  light  filters  must  not 
be  red  and  green  and  violet,  but  rather  red  and  yellow  and 
blue.  The  difference  arises  from  the  fact,  well  known  to 
every  student  of  color,  that  you  get  a  different  effect  by 
mixing  lights  and  by  superposing  pigments  of  the  same 
hues  as  the  lights.  If  you  mix  lights,  as  in  the  process  of 
stippling,  you  add  one  thing  to  another.  Red  and  green 
and  violet  waves  each  strike  upon  the  eye  and  produce 
a  color  sensation  of  definite  quality,  depending  on  the 
relative  intensities  of  the  different  lights.  If,  on  the  other 


COLOR  VISION  AND  COLOR  PHOTOGRAPHY          41 

hand,  you  mix  pigments,  you  subtract  one  thing  from  another. 
Superpose  violet  on  green  and  this  on  red.  To  estimate  the 
resultant  influence  on  the  eye,  you  have  to  consider  how 
much  of  the  red  is  taken  out  by  the  green  and  how  much 
more  of  these  two  is  subtracted  in  the  passage  through  the 
violet.  The  process  is  seen  to  be  subtractive,  and  you  would 
expect  the  result  to  be  different  from  the  additive  one  that 
takes  place  when  lights  are  mixed.  Experiment  shows 
clearly  that  there  is  a  difference,  and  it  was  because  the 
artists  used  a  subtractive  and  not  an  additive  process  that 
they  concluded,  as  we  have  seen,  that  the  primary  colors 
are  red  and  yellow  and  blue  instead  of  red  and  green  and 
violet. 

The  last  phase  (C)  of  the  process  has  still  to  be  referred 
to,  the  recomposition  of  the  three  elements  of  the  final 
picture.  This  is  done  by  superposing  the  three  colored 
films  obtained  as  already  described.  The  process,  how- 
ever, is  much  less  simple  than  it  appears  at  first  sight. 
When  the  three  films  are  superposed,  some  defect  in  one 
or  other  of  the  monochromes  is  almost  sure  to  be  revealed : 
the  red  may  be  too  intense  or  the  violet  too  faint,  or  there 
may  be  local  faults.  It  is  therefore  necessary  to  super- 
pose the  films  provisionally  in  order  that  such  defects  may 
be  revealed,  and  then  to  have  resort  to  various  expedients 
for  removing  the  defects.  When  the  best  has  been  accom- 
plished, the  films  must  be  very  carefully  placed  on  top  of 
one  another  so  as  to  fit  as  exactly  as  possible,  and  thus 
you  have  a  color  photograph  mounted  on  glass  or  on  paper, 
according  as  you  wish  to  view  it  as  a  transparency  or  not. 

You  will  have  realized,  no  doubt,  that  a  process  such  as 
that  described  requires  no  ordinary  care  and  skill.  Many 
of  the  operations  can  only  be  satisfactorily  performed  in 


42  LIGHT 

a  physical  laboratory,  with  the  instruments  of  precision 
and  the  skill  in  using  them  that  such  a  laboratory  affords. 
Under  such  circumstances,  color  photography  could  never 
become  a  popular  art.  Recently,  however,  a  process  due 
to  the  brothers  Lumiere  of  Paris  has  come  into  vogue,  and 
this  is  so  much  more  easily  carried  out  that  it  may  yet 
become  quite  popular.  It  is  no  longer  necessary  for  the 
photographer  to  concern  himself  with  the  complex  problems 
that  have  just  been  referred  to ;  most  of  these  problems 
have  been  solved  for  him  by  the  maker  of  the  autochrome 
plate,  as  it  is  called.  The  user  of  the  plate  has  little  more 
to  do  than  expose  and  develop  it,  as  he  would  in  the  pho- 
tography with  which  we  are  all  familiar. 

The  materials  employed  are  simple.  The  plate  is  care- 
fully coated  with  a  paste  made  from  potato  starch.  The 
starch  is  composed  of  fine  grains,  and  these  are  separated 
into  three  sets  and  dyed  respectively  red  and  green  and 
violet  —  for  the  process,  as  we  shall  see,  is  essentially  an 
additive  one.  When  mixed  together  in  equal  proportions, 
the  grains  form  a  powder  not  quite  white,  but  of  an  olive- 
gray  tint.  This  powder  is  scattered  on  a  glass  plate  on 
which  is  an  adhesive,  and  the  surplus  powder  removed  until 
there  is  left  only  a  single  layer  of  starch  grains  —  some  four 
million  to  the  square  inch.  This  layer  is  coated  with  var- 
nish, and  when  covered  with  a  sensitive  emulsion  of  the 
right  kind,  constitutes  the  autochrome  plate. 

How  does  such  a  contrivance  enable  us  to  reproduce  the 
colors  of  a  landscape?  The  explanation,  after  what  has 
been  said  already,  is  simple  enough.  The  starch  grains 
act  as  light  filters ;  we  may  say  approximately  that  the  red 
grains  filter  out  all  but  red,  the  green  all  but  green,  and  the 
violet  all  but  violet.  The  red  light  from  any  part  of  the 


COLOR  VISION  AND  COLOR  PHOTOGRAPHY          43 

landscape  will  filter  through  the  red  grains  only  and  reach 
the  sensitive  emulsion  behind  the  starch.  If  this  emulsion 
be  sensitive  to  red,  it  will  be  acted  upon  chemically,  and 
there  will  be  a  black  spot  behind  each  red  grain,  through 
which  the  light  has  come.  Suppose,  then,  that  light  were 
now  to  shine  from  behind  the  emulsion,  it  would  be  stopped 
by  the  black  spots,  and  wherever  red  was  present  in  the 
original  there  would  be  darkness  on  the  plate.  In  other 
words,  the  blackened  emulsion  constitutes  a  negative  of  the 
red  part  of  the  landscape.  This  negative  may  be  turned 
into  a  positive  by  processes  similar  to  those  employed  in 
ordinary  photography.  Wash  away  the  black  spots  and 
leave  them  colorless,  so  that  there  is  now  a  clear  space  be- 
hind the  red  grains  that  were  originally  affected.  If  now 
light  shines  through  from  behind,  we  should  have  a  positive 
of  the  red  part  of  the  picture.  What  is  true  of  the  red  is 
true  also  of  the  green  and  violet,  and  as  we  have  already 
seen  that  any  color  can  be  represented  by  suitable  com- 
binations of  these  three,  we  are  in  a  position  to  understand 
why  the  autochrome  plate  can  give  us  by  a  single  exposure 
a  perfect  picture,  however  complex  be  the  scheme  of  color. 
One  feature  of  the  process  may  require  some  comment. 
As  the  three  constituent  colors,  red  and  green  and  violet, 
are,  in  this  process,  necessarily  taken  together,  the  emul- 
sion must  be  as  nearly  as  possible  equally  sensitive  to  these 
three  colors.  You  must  know  that  this  is  certainly  not 
the  case  with  the  plates  you  use  in  ordinary  photography. 
Such  plates  are  highly  sensitive  to  violet,  and  scarcely 
sensitive  at  all  to  red  and  very  little  to  green.  The  fact 
that  they  are  insensitive  to  red  enables  you  to  carry  on  the 
development  in  a  red  light,  and  so  to  see  clearly  what  you 
are  doing.  The  Lumiere  emulsion  is  sensitive  to  red  and 


44  LIGHT 

green  about  equally,  but  it  is  much  more  sensitive  to  violet. 
To  overcome  this  difficulty,  at  least  in  part,  a  yellow  screen 
is  inserted  in  front  of  the  plate.  This  cuts  out  some  of  the 
violet  light,  and  by  diminishing  its  intensity  compensates 
in  a  measure  for  the  plate's  supersensitiveness  to  violet. 
With  this  device  the  plate  is  rendered  approximately  pan- 
chromatic. As  it  is  sensitive  to  all  colors,  you  must  work 
with  it  only  in  complete  darkness. 

In  a  moment  I  shall  show  you  a  large  collection  of  color 
photographs  taken  by  various  processes,  amongst  others 
by  that  just  described.  I  owe  them  to  the  courtesy 
of  a  student  of  Columbia  University,  who  has  made 
a  special  study  of  the  subject.  Before  showing  these, 
however,  a  few  further  remarks  with  reference  to  the  Lu- 
mieres'  latest  process  may  not  be  out  of  place.  (1)  As 
it  stands  to-day,  the  process  is  useless  except  for  trans- 
parencies. The  starch  paste  is  not  quite  transparent,  and 
absorbs  so  much  light  that  the  picture,  when  viewed  by 
reflection,  appears  almost  black.  (2)  The  process  will 
not  give  us  photographs  on  paper.  (3)  The  plate  that  is 
exposed  is  the  same  that  afterwards  presents  the  colored 
transparency.  Hence  a  separate  exposure  is  required  for 
each  picture,  and  there  can  be  no  multiplication  of  the 
same  photograph,  as  there  is  in  ordinary  photography. 
(4)  The  process  does  not  as  yet  lend  itself  to  the  art  of 
the  retoucher,  nor  permit  any  liberties  to  be  taken. 

[A  large  collection  of  color  photographs  was  here  exhibited.] 

After  seeing  such  pictures  as  these,  the  question  naturally 
arises,  What  are  the  relations  of  color  photography  at  its 
best  to  art  ?  Will  it  aid  the  art  of  painting,  or  is  there  any 
chance  that  it  may  seriously  rival  that  art,  and  possibly 


COLOR  VISION  AND  COLOR  PHOTOGRAPHY  45 

even  supersede  it?  Before  attempting  any  answer,  we 
must  remember  that  color  photography  is  still  in  its 
infancy,  and  we  must  make  reasonable  allowance  for 
the  improvements  that  are  sure  to  come  in  the  future. 
But  what  are  its  outstanding  defects  to-day?  Several  are 
suggested,  but  the  one  most  generally  emphasized  is  that 
a  color  photograph  is  still  somewhat  hard  and  metallic, 
that  it  lacks  the  softness  and  the  charm  of  a  real  work  of 
art.  Your  view  as  to  this  must  be  largely  a  matter  of  taste, 
and  perhaps  it  is  the  wisest  course  to  accept  the  maxim 
de  gustibus  non  est  disputandum.  Personally,  I  am  inclined 
to  doubt  whether  a  color  photograph  is  necessarily  hard, 
although,  of  course,  I  admit  that  it  often  is  so.  If,  however, 
this  hardness  really  exists  as  a  necessity,  and  not  as  a  mere 
accident,  it  is  not  easy  to  see  to  what  it  is  due.  There 
can  be  no  doubt  that  a  color  photograph  is  capable  of  giv- 
ing a  faithful  reproduction  of  each  detail  of  the  original,  and 
if  this  be  so,  why  should  not  the  whole  be  faithful,  and 
thus  as  soft  and  charming  as  the  original?  The  answer 
is  that,  possibly,  the  final  result  may  be  marred  by  an 
excessive  faithfulness  in  detail.  In  looking  at  a  landscape, 
the  eye  takes  it  in  as  a  whole  and  not  by  separate  parts. 
Every  color  is  modified  by  the  presence  of  all  the  others 
so  that  the  actual  appearance  of  a  single  leaf  is  somewhat 
different  from  what  it  would  be  were  you  to  isolate  the  leaf 
and  examine  it  alone.  Now  the  photographic  plate  sees 
by  isolating,  and  it  presents  the  exact  intensity  of  each  con- 
stituent color  as  it  is,  unmodified  by  the  presence  of  the 
rest.  It  may  be  the  failure  to  allow  for  the  subtle  influences 
of  neighboring  colors  that  produces  a  sense  of  harshness 
and  a  consequent  lack  of  charm.  But,  you  object,  the  eye 
looks  at  the  photograph  as  a  whole,  and  why,  then,  should 


46  LIGHT 

not  the  colors  in  the  photograph  react  on  one  another 
and  produce  the  same  effect  as  they  do  in  the  original? 
Perhaps  they  do  for  some,  but  it  may  not  be  so  for  every 
eye.  We  must  remember  that  there  is  an  important  dif- 
ference between  the  photograph  and  its  original :  the  one 
is  seen  as  a  flat  surface,  the  other  in  perspective.  The 
artist  may  be  able  to  surmount  the  consequent  difficulties 
by  taking  liberties  with  the  details  of  the  color,  while  the 
photographic  plate  is  fettered  by  being  bound  too  closely 
to  an  absolute  truth  of  detail. 

However,  even  if  this  be  so,  and  color  photographs  be 
thus  doomed  eternally  to  a  certain  harshness,  there  can,  I 
think,  be  little  doubt  that  some  day  they  will  form  a  seri- 
ous rival  to  all  but  the  highest  art.  Such  art  can  never  be 
endangered.  It  will  always  hold,  unchallenged,  the  great 
field  of  imaginative  painting  that  appeals  so  powerfully 
to  the  heart  and  mind,  whilst  in  the  realms  of  portraiture 
and  landscape  painting  there  must  always  be  moods  and 
phases  that  only  a  great  artist  can  seize  upon  and  express. 
This  will  be  the  work  of  the  few,  those  greatest  of  our  race 
who  show  us  aspects  of  things  that  otherwise  we  should 
wholly  miss,  and  delight  us  by  expressing  clearly  what  we 
only  indistinctly  feel. 


Ill 

DISPERSION   AND   ABSORPTION 

IN  the  first  lecture  of  this  course  I  showed  you  that  it  was 
possible  within  the  compass  of  a  single  minute  to  summarize 
all  the  knowledge  of  optical  principles  gained  by  man  from 
the  dawn  of  his  intelligence  until  Newton  appeared  in  the 
seventeenth  century  of  our  era.  One  of  the  few  general 
facts  known  in  pre-Newtonian  days  was  the  fact  of  Refrac- 
tion, the  fact,  namely,  that  a  beam  of  light  is  bent  in  passing 
from  one  medium  to  another,  as,  for  example,  from  air  to 
water.  By  considering  carefully  the  amount  of  bending, 
Newton  was  led,  as  we  have  seen,  to  a  clear  enunciation 
of  the  relation  between  refrangibility  and  color  and  to  a 
revelation  of  the  composite  character  of  a  beam  of  sunlight. 
The  white  beam  is  a  coat  of  many  colors,  and  each  color 
is  bent  differently  in  crossing  a  refracting  surface.  Thus, 
when  a  parallel  beam  of  sunlight  strikes  the  water,  the 
different  elements  are  spread  out  in  the  water.  This  is  the 
fact  of  dispersion.  It  has  already  been  brought  before  your 
notice  by  experiments.  Our  object  to-night  is  to  scruti- 
nize it  somewhat  more  closely  and  try  to  gain  a  clue  as  to 
the  reason  of  the  spreading  out  —  in  other  words,  we  seek 
a  theory  of  dispersion.  Before  setting  out  in  the  search,  it 
is  well  to  look  another  fact  in  the  face,  at  first  sight  a 
very  different  one,  although  a  closer  examination  reveals 
a  strong  family  likeness  between  the  two.  This  is  the 

47 


48  LIGHT 

fact  of  absorption,  and  particularly  the  fact  that  a  substance 
may  be  transparent  for  one  kind  of  light  and  opaque  for 
another  —  it  may  freely  transmit  blue  and  absorb  most  of 
the  red.  The  explanation  of  this  involves  a  theory  of 
absorption,  and  it  is  with  theories  of  absorption  and  dis- 
persion that  we  are  to  deal  exclusively  in  this  lecture. 

I  have  already  stated  that  a  modern  physicist  prefers 
to  speak  in  the  language  of  mechanics,  so  that  it  should 
cause  no  surprise  that  in  dealing  with  absorption  and  dis- 
persion we  take  certain  mechanical  principles  as  the  basis 
of  our  theories.  One  of  these  principles  is  so  important 
that  I  must  state  and  illustrate  it  as  fully  as  time  will  per- 
mit, for  unless  you  grasp  it  firmly,  you  cannot  hope  to  under- 
stand the  theories  that  will  be  presented  to  you;  whilst  if 
you  do  understand  it,  at  least  the  main  outlines  of  these 
theories  should  be  easily  and  clearly  seen.  Suppose  that 
you  have  a  system  of  bodies  at  rest,  and  that  you  disturb  it 
slightly  from  its  position  of  equilibrium.  If  that  position 
be  stable,  the  system  will  oscillate  to  and  fro  like  a  ship 
rocking  on  the  ocean,  with  a  definite  frequency  that  de- 
pends entirely  on  the  arrangement  of  the  system  and  the 
forces  that  act  upon  it.  This  frequency,  i.e.  the  number  of 
oscillations  per  second,  may  be  called  the  natural  frequency, 
as  it  depends  entirely  on  what  happens  when  the  system 
is  allowed  to  move  naturally,  without  any  interference  from 
without.  Suppose,  next,  that  by  outside  action  you  force 
an  oscillatory  motion  on  the  system.  The  frequency  of  this 
outside  action  is  entirely  at  your  disposal ;  you  can  make 
it  what  you  will,  and  may  find  it  convenient  to  style  it  the 
forced  frequency.  Now  the  mechanical  principle  that  I 
wish  to  emphasize  is  this:  the  disturbance  produced  in  a 
system  depends  on  the  frequency  of  the  oscillation  forced 


DISPERSION  AND  ABSORPTION  49 

upon  it,  and  is  very  much  greater  when  there  is  coincidence, 
or  nearly  coincidence,  between  the  forced  and  the  natural  fre- 
quencies than  when  this  is  not  the  case.  Perhaps  the  most 
familiar  illustration  presents  itself  in  the  problem  of  giving 
a  child  a  swing.  You  can  scarcely  have  failed  to  observe 
that  the  magnitude  of  the  swing  depends  very  largely  on 
how  your  pushes  are  timed. 
If  you  push  at  random,  you 
will  sometimes  help  the  swing 
and  sometimes  retard  it,  and 
the  work  that  you  do  will  be 
much  the  most  effective  if  you 
always  push  when  the  swing  is 
in  the  same  phase  of  its  to-and- 
fro  motion,  i.e.  if  you  arrange 
that  the  forced  frequency 
should  coincide  with  the  natu- 
ral one.  Here  is  a  simple  de- 
vice that  will  illustrate  the 
same  principle.  It  consists,  as 
you  see  (Fig.  5),  of  two  pen- 
dulums, A  and  B,  fastened  by  FlG'  5 
strings  to  a  not  very  rigid  support,  CD.  By  swinging 
either  pendulum,  you  see  that  its  natural  frequency 
depends  upon  its  length,  that  the  frequencies  of  the  two 
pendulums  are  the  same  when  the  lengths  are  the  same, 
and  that  by  varying  the  lengths  you  can  get  almost  any 
frequency  that  you  may  want.  Now  suppose  I  set  A  in 
motion  and  swing  it  at  right  angles  to  the  plane  A  CD, 
so  that  it  does  not  get  entangled  with  the  other  pendulum. 
As  A  moves  to  and  fro,  the  pull  in  the  string  AC  will  set  up 
a  vibration  in  the  support  CD,  and  this  will  be  communi- 


50  LIGHT 

cated  to  the  string  BD.  When  the  lengths  AC  and  BD 
are  very  different,  you  will  observe  that,  in  spite  of  the 
vibration  communicated  to  BD,  the  pendulum  B  remains 
practically  at  rest ;  you  see  no  signs  of  its  motion.  When, 
however,  the  lengths  AC  and  BD  are  nearly  equal,  B  be- 
gins to  show  signs  of  unrest,  and  it  moves  very  perceptibly 
when  the  strings  are  equally  long,  i.e.  when  the  forced  and 
the  natural  frequencies  coincide. 

As  another  simple  illustration  of  the  same  important 
principle,  consider  the  motion  of  water  in  a  bucket.  If 
it  be  at  rest  to  begin  with,  and  you  slightly  disturb  it,  the 
water  will  oscillate  backwards  and  forwards  with  a  natural 
frequency  that  is  easily  observed.  Now  take  the  bucket 
by  the  handle  and  carry  it  off.  As  you  step  along  regularly, 
each  time  that  your  foot  goes  down  you  will  give  a  slight 
jerk  to  the  handle  of  the  bucket,  and  this  will  be  communi- 
cated to  the  water.  Thus  forced  oscillations  will  be  set 
up,  their  frequency  depending  on  the  rate  at  which  you  walk. 
If,  by  design  or  by  accident,  you  time  your  treads  so  that 
their  frequency  coincides  with  the  natural  frequency  of  the 
water,  very  much  greater  disturbance  will  take  place  than 
would  otherwise  be  the  case,  and  if  the  bucket  be  nearly 
full,  a  good  deal  of  the  water  will  flop  over  the  edges. 

Other  illustrations  might  be  drawn  from  various  fields, 
for  the  principle  is  wonderfully  far-reaching,  and  enters 
into  the  explanation  of  countless  phenomena,  from  the 
trivial  one  just  mentioned  to  some  of  the  most  stupendous 
and  awe-inspiring  catastrophes  that  human  history  records 
or  the  study  of  celestial  mechanics  reveals.  To-night  we 
have  no  time  to  enter  further  into  the  matter,  except  to 
bring  before  you  one  more  simple  experiment  as  a  final 
illustration  of  the  same  underlying  principle.  A  (Fig.  6) 


DISPERSION  AND  ABSORPTION 


51 


is  an  organ-pipe,  the  end  of  which  is  closed  by  a  thin  film, 
formed  by  dipping  the  pipe  into  a  soapy  solution.  If  the 
air  within  the  pipe  be  disturbed  in  any  way,  it  will  oscillate 
to  and  fro  with  a  natural  frequency  that  depends  on  the 
form  and  dimensions  of  the  pipe.  These  oscillations  will 


B 


FIG.  6 

cause  the  film  to  pulsate,  and  the  character  of  these  pulsa- 
tions is  revealed  by  allowing  a  beam  of  light  to  be  reflected 
from  the  film  on  to  a  screen  at  S.  By  watching  the  move- 
ment on  the  screen,  you  can  judge  whether  there  is  much 
throbbing  of  the  film  or  not.  Now  let  us  force  oscillations 
on  pipe  A  by  means  of  vibrations  in  another  organ-pipe 
B,  and  vary  the  frequency  of  these  vibrations  by  altering 
the  length  of  this  second  pipe.  You  will  observe  that  the 
disturbance  revealed  by  looking  at  the  screen  is  enormously 
more  violent  when  the  forced  and  natural  frequencies 
coincide  than  when  they  are  widely  different.  Here,  as 
before,  you  see  that  for  many  purposes  the  magnitude  of  a 
shake  is  less  important  than  its  frequency,  and  that  a  small 


52 


LIGHT 


At 

frequency 


FIG.  7 


vibration  rightly  timed  may  set  up  far  more  disturbance 
than  a  large  one  with  a  different  frequency. 

Bearing  this  principle  in  mind,  imagine  that  you  are 
watching  a  fleet  of  ships  upon  the  ocean,  and  that,  to  begin 
with,  all  is  calm.  Then  suppose  that  each  is  slightly  dis- 
turbed, as  by  the  shifting  of  machinery  or  cargo.  Each 
ship  will  rock  to  and  fro,  with  a  natural  frequency  depend- 
ing on  the  shape  of  the 
vessel  and  the  arrange- 
ment of  its  cargo.  If  all 
the  ships  be  similar,  they 
will  all  rock  with  the 
same  frequency.  Now 
D  %  imagine  a  series  of  waves 

to  come  along  and  strike 
upon  these  moving  ships. 
They  will  continue  to  rock,  and  if  the  frequency  of  the  in- 
coming waves  be  very  different  from  the  natural  frequency  of 
the  ships,  there  will  be  little  change  in  the  motion.  Suppose, 
however,  the  frequency  of  the  waves  is  gradually  changed. 
As  it  approaches  that  of  the  natural  frequency  of  the  ships, 
the  motion  will  be  much  more  violent,  and  will  be  most 
marked  when  the  natural  and  forced  frequencies  are  the 
same.  Once  this  stage  is  passed,  and  the  forced  frequency 
begins  to  differ  largely  from  the  natural  one,  the  oscillations 
will  die  down,  and  in  time  you  will  return  to  calmness  and 
to  comfort.  If  you  care  to  represent  things  graphically, 
you  may  indicate  the  forced  frequencies  by  distances 
measured  horizontally  along  the  line  ABODE  of  Fig.  7, 
and  the  corresponding  disturbances  by  lines  drawn  ver- 
tically. You  then  get  a  figure  such  as  is  here  presented, 
where  C  corresponds  to  the  natural  frequency  of  the 


DISPERSION  AND  ABSORPTION  53 

ship's  oscillation;  and  most  of  the  disturbance  is  confined 
to  a  somewhat  narrow  range,  BD,  in  the  neighborhood  of  C. 
In  the  region  where  the  disturbance  is  considerable,  the 
ships  are  rocking  violently,  and  are  therefore  capable  of 
doing  a  large  amount  of  work.  In  technical  language, 
they  have  great  energy.  This  energy  must  come  from 
somewhere,  and  its  only  possible  source  is  the  motion  of 
the  sea  waves.  Under  these  circumstances,  a  great  deal 
of  energy  must  be  absorbed  from  the  water  waves,  so  that 
in  the  region  beyond  the  ships  you  would  observe  a  com- 
parative calm.  You  have  only  to  apply  the  same  principles 
to  the  waves  in  the  ether  that  give  us  the  sensation  of  light 
to  understand  how  a  substance  may  absorb  most  of  the 
light  of  one  color,  and  be  practically  transparent  to  every 
other  kind  of  light.  In  this  case  the  ships  are  replaced 
by  the  atoms  of  matter,  or  rather,  according  to  modern 
views,  each  atom  is  a  whole  fleet  of  ships.  The  old  atom  of 
chemistry  is  now  replaced  by  a  group  of  electrons,  which 
move  about  like  the  stars  in  a  cluster,  and  could  they  be 
seen,  might  appear  as  the  Pleiades  ''glittering  like  a  swarm 
of  fireflies  tangled  in  a  silvery  braid."  If  the  ether  waves 
have  a  frequency  nearly  coincident  with  the  natural  fre- 
quency of  the  electrons,  they  do  so  much  work  in  disturbing 
these  electrons  that  their  energy  is  almost  all  spent.  They 
have  not  enough  left  to  stimulate  the  optic  nerve,  and  we 
see  no  light.  On  the  screen  is  thrown  the  familiar  spectrum 
caused  by  sending  a  beam  of  white  light  through  a  trans- 
parent prism  of  glass.  There  is  no  appreciable  absorption 
for  any  color ;  the  spectrum  is  continuous,  with  every  color 
of  the  rainbow  represented.  Now  let  the  same  light  pass 
also  through  this  chemical  solution,  and  observe  the  change 
in  the  spectrum.  A  portion  of  the  yellow  is  cut  out  and 


54  LIGHT 

replaced  by  absolute  blackness,  so  that  this  kind  of  light  is 
absorbed  by  the  solution,  while  all  other  kinds  come  through 
just  as  before.  Are  we  not  justified  in  concluding,  in  view 
of  all  that  has  gone  before,  that  the  natural  frequency  of 
the  electrons  in  the  solution  is  the  same  as  the  frequency 
in  the  ether  waves  corresponding  to  this  portion  of  the 
yellow  ? 

In  the  case  that  we  have  considered,  where  there  is  a 
single  moving  object,  such  as  a  ship,  there  may  be  only 
one  natural  frequency,  but  with  a  more  complex  mechan- 
ism the  natural  frequencies  may  be  many.  If  you  regard 
the  principal  planets  of  the  solar  system  as  forming  a  single 
mechanism,  each  of  the  eight  constituents  goes  through 
regular  periodic  movements  with  a  definite  frequency. 
Thus,  in  their  motion  round  the  Sun,  they  observe  a  strict 
and  invariable  law,  Mercury  taking  88  days  (in  round  num- 
bers), Venus  225,  the  Earth  365,  and  so  on  to  Neptune, 
with  the  lengthy  period  of  60,127  days.  Imagine,  then,  a 
mighty  system  of  waves  running  across  the  solar  system. 
If  the  frequency  were  such  that  the  waves  oscillated  once  in 
88  days,  most  of  the  energy  of  the  waves  would  be  absorbed 
in  dashing  the  planet  Mercury  to  and  fro,  while  the  other 
planets  would  be  comparatively  little  affected.  If,  how- 
ever, the  waves  oscillated  once  in  a  year,  our  earth  would 
be  responsible  for  the  absorption  of  energy,  and  similarly 
for  other  frequencies.  Suppose,  now,  that  the  impinging 
waves  had  all  possible  frequencies.  They  would  all  pass 
through  the  solar  system  practically  unmodified,  except 
the  eight  with  frequencies  corresponding  to  the  periodic 
movements  of  the  planets.  These  eight  would  have  their 
energy  absorbed  in  disturbing  the  planets,  and  they  would 
be  relatively  small  and  insignificant  in  the  region  of  space 


DISPERSION  AND  ABSORPTION  55 

beyond  the  solar  system.  In  exactly  the  same  way  will 
light  be  absorbed  by  a  substance,  those  colors  being 
cut  out  that  correspond  to  frequencies  identical  with  the 
various  natural  frequencies  of  the  complex  group  of  elec- 
trons composing  the  substance.  In  Fig.  8  you  will  see  how 
many  dark  bands  there  are  in  the  spectra  of  some  simple 
substances,  and  if  you  realize  that  each  of  those  dark  lines 


Nitrous  fumes 


•Illlll 


II 


Vapour  of  Iodine 
FIG.  8 


indicates  a  different  natural  frequency,  you  will  understand, 
in  a  measure,  how  complex  must  be  the  motions  going  on 
within  the  atom,  and  how  formidable  the  task  of  the  man 
of  science  who  tries  to  master  its  mechanism. 

Here  you  get  a  glimpse  into  a  field  of  great  interest  and 
promise.  The  principle  of  fundamental  importance  is 
that  the  position  of  the  absorption  bands  in  the  spectrum 
of  any  substance  gives  us  information,  and  very  definite 
information,  as  to  the  frequencies  of  the  vibrations  that  go 
on  within  its  atoms.  If  we  knew  the  nature  of  those  atoms, 
we  could,  were  our  mathematics  sufficiently  developed, 
calculate  the  frequencies  of  the  vibrations.  At  present 
we  are  trying  to  reverse  the  process,  and  seek  tne  unknown 
from  the  known,  and  the  time  may  yet  come  when  we  can 
speak  confidently  of  the  minutest  movements  within  the 


56  LIGHT 

atom.  That  time  is  certainly  not  yet,  and  probably  for 
long  we  must  devote  ourselves  with  patient  labor  to  ac- 
cumulating facts  that  bear  upon  the  problem.  Much  has 
already  been  done,  and  the  positions  of  the  absorption  bands 
for  many  substances  have  been  accurately  observed  over  a 
wide  range  of  frequencies.  Let  me  call  your  attention  to  a 
few  of  the  suggestive  results  that  have  thus  been  reached. 
(1)  The  lines  in  the  spectrum  are  not  arranged  at  random, 
but  accorcfeig  to  laws  which  are  more  or  less  simple  with 
different  elements.  The  simplest  case  is  that  in  which  the 
relation  between  the  frequencies  corresponds  exactly  to  the 
relation  between  a  fundamental  note  and  its  harmonics. 
Strike  the  middle  C  of  a  piano,  and  you  set  up  a  to-and-fro 
motion  in  the  air,  there  being  256  vibrations  in  a  second, 
so  that  the  frequency  is  256.  If  you  strike  exactly  an  octave 
higher,  you  double  the  frequency.  It  is  found  that  the 
lines  in  the  spectra  of  some  substances  are  arranged  so  that 
the  frequency  corresponding  to  one  line  is  exactly  double 
that  of  the  other.  If,  however,  you  take  all  the  lines  into 
consideration,  the  relation  between  them  is  much  more 
complex.  One  of  the  best-known  examples  is  afforded 
by  the  spectrum  of  hydrogen.  In  1885  Balmer  showed 
that  the  frequencies  corresponding  to  the  different  lines  were 
all  given  by  the  formula,  frequency  =  a  (1— 4/n2),  where  a 
is  a  constant  and  n  any  integer  greater  than  2.  At  this 
time  only  9  lines  had  been  observed,  but  as  the  number 
was  extended  beyond  30,  it  was  found  that  Balmer's  law 
still  fitted  the  observations  admirably.  Thus,  hydrogen 
seemed  to  present  a  unique  example  of  simplicity,  all  the 
lines  in  its  spectrum  being  connected  by  the  same  simple 
law.  However,  the  later  speculations  of  other  physicists, 
particularly  Rydberg,  Kayser,  and  Runge,  made  it  seem 


DISPERSION  AND  ABSORPTION  57 

probable  that  other  lines  existed,  although  they  had  not  yet 
been  observed.  This  was  confirmed  in  a  striking  way  by 
Pickering  in  1896,  while  examining  the  spectrum  of  a  star 
that  shows  the  hydrogen  lines  strongly.  He  found  a  new 
series  of  lines  related  to  the  old  ones  in  just  the  way  that  had 
been  anticipated. 

(2)  It  is  found  that  with  several  elements  the  lines  in 
the  spectrum  are  arranged  in  groups  of  twos  or  threes, 
forming  doublets  or  triplets,  as  they  are  called,  and  that 
the  difference  in  the  frequencies  of  the  two  members  of  a 
doublet  is  the  same  for  each  group,  with  a  similar  law  for 
triplets. 

(3)  Where  the  lines  are  not  arranged  in  doublets  or 
triplets,  they  often  appear  in  two  different  series.     There 
is  a  series  of  sharp  lines  connected  by  one  law,  and  another 
series  of  diffuse  lines  connected  by  a  different  law. 

(4)  The  regularity  in  the  spectra  of  some  elements,  e.g. 
tin,  lead,  arsenic,  antimony,  bismuth,  and  platinum,  con- 
sists in  the  recurrence  of  certain  constant  differences  of  fre- 
quency between  the  lines. 

(5)  In  what  are  known  as  band  spectra,  when  the  fluted 
spectrum  is  resolved  by  higher  dispersion  into  groups  of 
fine  lines,  it  is  often  found  that  the  frequencies  obey  a  very 
simple  law.    They  form  an  arithmetical  series,  i.e.  each  fre- 
quency differs  from  its  predecessor  by  a  constant  difference. 
On  careful  examination,  it  appears  that  the  spectrum  is  made 
up  by  repetitions  of  similar  groups  of  lines,  and  it  seems 
probable  that  the  number  and  distribution  of  the  lines  in 
each  group  depend  on  the  number  and  distribution  of  the 
atoms,  or  of  the  electrons  that  compose  these  atoms. 

(6)  Lastly,  various  relations  have  been  suggested  between 
the  atomic  weights  of  different  substances  and  their  natural 


58       -"•'•-.  LIGHT 

frequencies.  Kayser  and  Runge  have  concluded  that  in  the 
case  of  elements  of  the  same  chemical  family  which  show 
a  series  of  doublets  in  their  spectra,  the  constant  difference 
of  frequencies  between  the  two  members  of  the  doublets 
is  very  nearly  proportional  to  the  squares  of  the  atomic 
weights.  Marshall  Watts  has  shown  that  with  the  class  of 
elements  that  contains  mercury,  cadmium,  and  zinc,  the 
ratio  of  the  difference  between  the  frequencies  of  certain 
lines  of  one  element  to  the  difference  between  the  frequen- 
cies of  the  corresponding  lines  of  the  other  element  is  the 
same  as  the  ratio  of  the  squares  of  their  atomic  weights. 
Morse,  of  Columbia  University,  has  found  that  if  you  take  a 
series  of  carbonates  with  different  chemical  bases — carbon- 
ates of  magnesium,  of  calcium,  of  iron,  of  zinc,  and  so  on,  you 
discover  a  very  simple  relation  between  the  atomic  weight  of 
the  base  and  the  frequency  that  is  determined  from  the 
position  of  the  absorption  band,  and  that  there  is  a  similar 
law  for  the  nitrates  and  the  sulphates  of  the  different  bases. 
These  various  facts  that  have  been  marshalled  are,  as  I 
have  said,  highly  suggestive,  and  they  will  inevitably  be 
made  the  basis  of  many  future  speculations  as  to  the  nature 
of  the  atom.  One  thing  at  least  they  show  us  very  clearly, 
namely,  that  in  the  little  kingdom  of  an  atom,  just  as  in 
the  mighty  realm  of  the  Sun,  law  is  supreme.  In  many 
cases  we  have  found  the  law,  but  there  is  much  yet  to  be 
done  to  fit  it  into  our  other  knowledge.  At  present  we  have 
only  glimpses  as  to  how  this  may  be  accomplished ;  but  we 
see  enough  to  give  us  hope  that  somewhere  in  the  future  the 
foundations  of  a  new  chemistry  will  be  firmly  laid.  Then 
we  shall  know  the  movements  of  the  atoms  and  the  laws 
that  govern  them  as  definitely  as  now  we  know  the  orbits  of 
the  planets  and  the  forces  that  confine  them  there. 


DISPERSION  AND  ABSORPTION  59 

Having  delayed  so  long  over  absorption,  I  must  hurry 
on  to  deal  with  dispersion,  the  theory  of  which  I  undertook 
to  discuss  at  the  beginning  of  this  lecture.  One  aspect  of 
that  theory  is  simple  enough :  it  is  the  aspect  usually  pre- 
sented exclusively  in  elementary  text-books  on  light. 
They  tell  us  that  dispersion  is  due  to  the  fact  that  where 
there  is  no  matter  present,  waves  of  light  all  move  with  the 
same  speed,  whatever  be  their  frequency  (or  color),  but 
that  they  move  with  different  speeds  in  any  material  such 
as  glass  or  water.  This  is  true  and  very  important,  but  it 
is  no  explanation.  It  does  not  go  deep  enough,  for  we  want 
to  know  why  these  facts  should  be  as  stated.  Before 
entering  upon  this,  however,  it  will  be  well  to  see  clearly 
that  the  fact  of  different  speeds  for  different  frequencies 
necessarily  leads  to  dispersion.  A  simple  analogy  may  help 
you  to  understand  the  phenomena.  Suppose  that  you 
watch  a  column  of  soldiers  marching  steadily  at  the  rate  of  4 
miles  an  hour,  and  that  when  they  cross  a  certain  line  they 
come  upon  ground  that  is  so  much  rougher  that  they  ad- 
vance at  the  rate  of  only  3  miles  an  hour.  What  would  be 
the  effect  of  this  on  an  observer  looking  from  a  distance, 
and  fixing  his  attention  on  the  front  of  the  column?  Let 
ST  in  Fig.  9  represent  the  line  that  divides  the  smooth 
from  the  rough  ground,  and  E,  F,  G,  H,  and  similar  letters, 
the  positions  of  different  soldiers  at  different  times.  If  the 
front  of  the  column  was  at  EQ  FQ  GQ  HQ  at  any  time,  then 
an  hour  later  it  would  be  at  EFGH,  where  EQ  E  is  4 
miles.  An  hour  later  than  this  H  would  be  at  HI  (4 
miles  from  H),  but  E  would  have  covered  only  3  miles 
on  the  rougher  ground,  and  would  be  at  El  where  EEl  is 
3  miles.  F  and  G  would  be  at  Flt  and  G?1,  as  shown  in 
the  figure,  having  walked  partly  over  smooth  and  partly 


60 


LIGHT 


over  rough  ground.  The  front  of  the  column  would  be  rep- 
resented by  the  line  E1}  Fl}  Gly  Hv  This  is  not  parallel  to 
EFGH,  so  that  the  column  would  have  changed  its  front, 
and  instead  of  moving  in  the  direction  EE1}  it  would  appear 
to  be  making  along  the  direction  ER,  where  ER  is  at  right 


angles  to  the  front.  If  then  you  were  describing  the  direc- 
tion in  which  the  column  was  tending,  you  might  say  that 
this  direction  was  broken  or  refracted  in  crossing  the  line 
ST.  It  is  not  difficult,  but  I  have  no  time  for  this  now,  to 
show  that  a  similar  result  would  be  looked  for  with  a  ray 
of  light  on  the  theory  of  wave-motion.  I  trust  that  you  can 
supply  this  step  in  the  argument,  and  convince  yourselves 
of  the  fact  that  refraction  is  at  once  accounted  for  by  a 
change  of  velocity  on  crossing  from  one  medium  into  the 
other.  The  step  to  dispersion  is  immediate  and  obvious. 
The  amount  that  the  column  changes  its  front  depends,  as 


DISPERSION  AND  ABSORPTION  61 

you  see,  on  the  speed  with  which  the  men  walk  on  crossing 
the  boundary  line  ST.  If  they  meet  with  even  rougher 
ground  than  before,  so  that  they  move  more  slowly,  the 
change  of  front  will  be  greater  than  before.  Thus,  suppose 
that  the  column  is  composed  of  two  sets  of  men,  one  in 
blue  and  the  other  in  red  uniforms,  and  that  until  they  reach 
the  rough  ground  they  advance  together  at  the  same  rate. 
(This  corresponds  to  the  fact  that  in  free  space,  where  there 
is  no  matter,  waves  of  light  of  all  colors  have  the  same 
velocity.)  After  crossing  the  line  ST,  let  the  red  men  walk 
at  3  and  the  blue  at  2  miles  per  hour.  The  latter  will 
separate  from  the  former,  and  will  form  a  new  column, 
whose  front  is  in  the  direction  E2  F%  <72  Hv  in  the  figure,  and 
which  therefore  appears  to  be  moving  in  the  direction  EB. 
The  columns  will  disperse  in  different  directions,  EH  and 
EB,  and  if  you  apply  similar  reasoning  to  the  case  of 
waves  of  light,  you  will  understand  how  dispersion  is 
accounted  for,  provided  only  you  can  see  that  waves  of 
different  frequencies  may  have  different  speeds  in  the  same 
medium. 

This  dependence  of  the  speed  of  a  wave  on  its  frequency, 
on  which  we  have  just  seen  that  any  explanation  of  dis- 
persion must  be  based,  is  no  simple  or  obvious  thing.  It 
has  occupied  the  minds  of  leading  physicists  for  nearly 
a  century  and,  in  spite  of  all  their  labors,  I  am  not  sure 
that  even  now  we  thoroughly  understand  it.  There  is  an 
initial  difficulty  that  is  very  formidable.  Think  of  a  beam 
of  light  passing  through  water  or  a  piece  of  glass.  The 
water  and  the  glass  look  thoroughly  homogeneous,  and 
even  if  you  examine  them  with  the  most  powerful  mi- 
croscope, you  will  get  no  direct  evidence  that  one  of  the 
smallest  parts  differs  in  any  essential  way  from  another. 


62  LIGHT 

Now  if  waves  of  any  kind  are  propagated  in  a  homogeneous 
medium,  it  is  difficult,  if  not  quite  impossible,  to  see  how 
their  speed  can  depend  on  their  frequencies.  However,  we 
have  to  face  the  fact  of  dispersion,  and  this,  if  nothing  else, 
would  drive  us  to  consider  the  possibility  of  matter,  such 
as  glass  or  water,  being  other  than  homogeneous.  In  its 
ultimate  analysis  we  shall  take  it  to  be  coarse-grained,  and 
see  how  this  will  help  us.  The  grains,  or  atoms,  we  shall 
regard  as  obstacles  in  the  path  of  the  waves  affecting  their 
progress.  Some  insight  into  the  matter  might  be  obtained 
by  thinking  of  a  column  of  soldiers  marching  through  a  for- 
est ;  their  rate  of  progress  would  obviously  depend  in  some 
measure  upon  the  distance  between  the  trees.  A  far 
more  instructive  study  for  our  purposes  would  be  to  observe 
carefully  the  rate  at  which  waves  were  propagated  in  water 
in  which  floats  are  placed  at  regular  intervals.  If  you  do 
this,  you  will  find  that  the  speed  of  the  wave  depends  upon 
its  frequency,  and  that  if  you  keep  the  floats  always  at 
the  same  distance,  but  modify  the  frequency,  you  alter 
the  speed  of  the  wave.  This  is  just  what  you  want  for  dis- 
persion, and  you  may  naturally  think  that  you  have  found 
the  key  that  unlocks  the  secret.  So,  no  doubt,  thought 
Cauchy  when,  early  last  century,  he  took  up  the  problem 
and  hit  on  this  idea.  But  the  way  of  the  physicist  is  hard, 
and  his  lot  is  made  peculiarly  difficult  by  the  duty  that  he 
has  imposed  upon  himself  of  living  up  to  a  very  high  stan- 
dard. He  is  not  content  with  mere  descriptive  theories, 
he  strives  to  state  them  in  the  strict  language  of  mathe- 
matics and  to  obtain  therefrom  a  formula.  From  such  a 
formula  definite  numerical  results  can  be  calculated  and  a 
close  and  accurate  comparison  made  between  theory  and 
observation.  The  object  of  a  dispersion  theory  is  to  build 


DISPERSION  AND  ABSORPTION  63 

up  from  some  rational  basis  a  formula  that  will  enable  us 
to  calculate  the  velocity  of  light  for  waves  of  different  fre- 
quencies, and  to  obtain  results  that  agree  as  closely  as  pos- 
sible with  what  is  derived  from  experiment.  Instead  of 
calculating  the  velocity  directly,  it  is  convenient  for  some 
purposes  to  estimate  the  ratio  of  the  velocity  of  light-waves 
in  free  space  to  that  of  waves  of  the  same  frequency  in  the 
matter  under  consideration,  e.g.  glass.  This  ratio  is  called 
the  refractive  index  of  the  matter,  and  we  shall  denote  it 
by  the  symbol  n.  As  light  has  the  same  velocity  for  all 
frequencies  in  free  space,  and  this  velocity  is  known, 
the  velocity  corresponding  to  any  frequency  in  a  material 
such  as  glass  is  at  once  obtained  by  dividing  the  known 
velocity  in  free  space  by  the  refractive  index  of  the  glass. 
The  refractive  index  (n)  will  depend  on  the  frequency  (/), 
and  any  dispersion  formula  gives  the  relation  that  exists 
between  n  and  /  on  the  basis  of  the  theory  considered. 
Cauchy  's  theory  led  him  to  a  dispersion  formula  of  this 
kind  :  — 


where  K,  a,  b,  .  .  .  are  constants  in  any  given  material,  but 
change  if  we  pass  from  one  material  to  another,  as  from 
glass  to  water.  On  putting  this  formula  to  the  test  of 
comparison  with  experimental  results,  Cauchy  and  his 
immediate  followers  found  that  it  stood  the  test  well,  so 
that  the  problem  of  dispersion  seemed  to  be  solved.  And 
yet  to-day  the  position  occupied  by  Cauchy  has  been 
wholly  abandoned,  and  you  may  well  ask  why.  I  have 
time  to  touch  on  only  three  reasons  to  account  for  the  fact 
that  it  has  been  necessary  to  look  for  some  other  theory  of 
dispersion  than  the  one  that  we  are  now  discussing. 


64  LIGHT 

(1)  In  the  first  place,  it  must  be  noted  that  the  obser- 
vations were  confined  to  a  somewhat  narrow  range  of  fre- 
quencies.   They  were  all  in  the  neighborhood  of  the  vis- 
ible spectrum,  the  frequencies  varying  in  round  numbers 
from  400  to  800  million  million.    Such  frequencies  are 
specially  interesting,  from  the  fact  that  they  alone  produce 
in  the  human  eye  the  sensation  of  light.    But  waves  of 
other  frequencies  are  easily  set  up  and  their  influence 
detected.    If  their  frequencies  be  high,  they  are  specially 
active  in  affecting  a  photographic  plate,  while  if  low,  they 
show  themselves  in  the  form  of  radiant  heat.    There  is,  of 
course,  no  reason  why  waves  of  such  frequencies  should 
be  subject  to  any  different  law  from  that  which  holds 
for  frequencies  that  give  the  sensation  of  light.    Thanks 
to  the  patience  and  the  ingenuity  of  modern  physicists,  we 
have  by  this  time  immensely  extended  the  range  of  ob- 
servation of   refractive    indices.    In   a   few   moments    I 
shall    refer    you    to    such    indices    accurately    observed 
for  frequencies  varying  from  about  13  million  million  to 
over  600  million  million.    Over  such  a  wide  range  Cauchy's 
formula  proves  to  be  extremely  ill  adapted  to  represent 
the  facts. 

(2)  The  second  objection  to  Cauchy's  formula  arises 
from  a  careful  examination  of  his  fundamental  idea.    That 
idea,  as  already  stated,  is  that  the  velocity  of  a  wave  must 
be  affected  by  the  relation  between  its  frequency  and  the 
distance  between  neighboring  molecules.     Assuming  this, 
and  noting  the  values  of  the  constants  in  Cauchy's  formula 
that  are  required  to  make  it  fit  as  well  as  possible  with  the 
observed  facts,  we  can  estimate  approximately  the  distance 
between  consecutive  molecules  in  any  substance.    Now 
there  are  other  and  much  surer  ways  of  estimating  these 


DISPERSION  AND  ABSORPTION  65 

distances,  and  it  is  found  that  Cauchy's  formula  separates 
the  molecules  far  too  widely.  In  a  given  length  it  would 
place  only  one  where  we  have  good  reason  for  supposing 
that  there  are  about  thirty  molecules. 

(3)  Thirdly,  Cauchy's  theory  gives  us  no  clue  to  the  con- 
nection between  absorption  and  dispersion,  and  these,  from 
many  points  of  view,  we  now  see  to  be  intimately  related 
phenomena. 

I  have  not  time  to  do  more  than  indicate  the  character 
of  more  modern  theories  of  dispersion  that  endeavor  to 
avoid  these  difficulties.  The  fundamental  idea  with 
them  all  is  that  the  molecules,  or,  according  to  the  more 
recent  theories,  the  atoms,  are  complex  structures,  the  parts 
of  which  can  vibrate  to  and  fro  with  definite  natural  fre- 
quencies. Thus  in  the  group  of  electrons  constituting  an 
atom,  each  member  may,  under  normal  circumstances, 
move  steadily  in  an  orbit,  like  a  planet  round  the  Sun. 
When  a  wave  strikes  such  a  system,  its  speed  will  be  affected 
just  as  in  Cauchy's  theory,  mainly  by  two  things:  first, 
the  displacement  that  the  wave  produces  in  the  moving 
member;  and  second,  the  magnitude  of  the  force  that 
tends  to  restore  that  member  to  its  orginial  position. 
When  dealing  with  absorption,  we  had  reason  to  emphasize 
the  fact  that  the  displacement  produced  by  the  impinging 
wave  would  depend  very  largely  on  the  relation  between  its 
frequency  and  the  natural  frequency  of  the  moving  system. 
Well-established  dynamical  principles  lead  us  easily  to  a 
formula  for  the  displacement  corresponding  to  any  given 
frequency,  and  the  only  matter  about  which  we  are  in 
doubt  is  the  character  of  the  force  that  tends  to  restore  a 
disturbed  element  to  its  original  orbit.  We  find  that  if 
the  frequency  (/)  is  not  very  close  to  any  of  the  natural 


66  LIGHT 

frequencies  (/i/2"0  of  the  system,  then  the  refractive  index 
(n)  should  be  given  by  the  formula  — 


, 

/"-/a2 

Here  a,  K,  Alf  and  A2  are  constants  for  any  given  material, 
the  value  of  a  depending  on  the  nature  of  the  intermo- 
lecular  forces  as  to  which  we  are,  as  yet,  more  or  less  in 
ignorance.  The  following  table  will  show  you  how  this 
formula  fits  in  with  the  facts  as  observed  in  the  case  of 
rock-salt,  a  substance  chosen  because  we  know  its  refractive 
indices  over  an  enormous  range  of  frequencies.  You  will 
observe  that  throughout  the  whole  range,  theory  and  ob- 
servation agree  within  the  limits  of  experimental  error. 

It  must  be  understood  that  the  six  constants  ^4.  1;  A2,fv 
/2,  a,  K  are  determined  so  as  to  make  the  formula  fit  the  facts 
for  six  arbitrarily  chosen  values  of  the  frequency  (/),  and 
that  the  formula  is  tested  by  noting  how  close  is  its  agree- 
ment with  the  remaining  60  observations,  there  being  66 
of  such  observations  in  all.  But  there  are  other  collateral 
tests.  The  constants  /x  and/2,  calculated,  be  it  remembered, 
from  observations  of  refractive  indices  alone,  denote  the 
natural  frequencies  of  parts  of  the  molecule.  We  have 
seen,  in  the  discussion  on  absorption,  that  these  frequencies 
determine  the  position  of  the  absorption  bands  of  the  sub- 
stance. Now  the  frequencies  corresponding  to  the  absorp- 
tion bands  can  be  determined  by  direct  experiment,  and 
it  is  found  that  they  agree  as  closely  as  could  be  desired 
with  the  values  calculated  from  the  above  formula.  Again, 
if  you  look  at  the  formula,  you  will  observe  that  when  the 
frequency  is  zero,  so  that/  =  0,  we  have  n2  =  K.  If  the  fre- 
quency is  zero,  that  means  that  there  are  no  vibrations  per 


DISPERSION  AND  ABSORPTION 


/ 

(in  million 
millions) 

n 
(theory) 

n 
(observation) 

/ 

(in  million 
millions) 

n 
(theory) 

n 

(observation) 

617 

1.5533 

1.5533 

255 

1.5303 

1.5303 

609 

1.5526 

1.5526 

250 

1.5302 

1.5301 

607 

1.5525 

1.5525 

238 

1.5297 

1.5297 

602 

1.5519 

1.5519 

228 

1.5294 

1.5294 

580 

1.5500 

1.5500 

202 

1.5285 

1.5285 

578 

1.5499 

1.5499 

193 

1.5582 

1.5281 

569 

1.5491 

1.5491 

183 

1.5278 

1.5278 

558 

1.5482 

1.5482 

170 

1.5274 

1.5274 

542 

1.5469 

1.5469 

145 

1.5265 

1.5265 

530 

1.5458 

1.5458 

137 

1.5263 

1.5262 

525 

1.5455 

1.5455 

133 

1.5261 

1.5261 

521 

1.5452 

1.5452 

127 

1.5258 

1.5258 

518 

1.5450 

1.5450 

96 

1.5241 

1.5240 

512 

1.5445 

1.5445 

92 

1.5237 

1.5237 

509 

1.5443 

1.5443 

89 

1.5235 

1.5235 

491 

1.5430 

1.5430 

83 

1.5229 

1.5229 

469 

1.5414 

1.5414 

79 

1.5224 

1.5224 

457 

1.5406 

1.5406 

73 

1.5216 

1.5216 

436 

1.5393 

1.5393 

64 

1.5200 

1.5197 

417 

1.5381 

1.5381 

57 

1.5183 

1.5180 

394 

1.5368 

1.5368 

52 

1.5155 

1.5159 

375 

1.5358 

1.5358 

44 

1.5123 

1.5121 

356 

1.5348 

1.5348 

42 

1.5103 

1.5102 

339 

1.5340 

1.5340 

40 

1.5086 

1.5085 

332 

1.5336 

1.5336 

37 

1.5063 

1.5064 

308 

1.5325 

1.5325 

35 

1.5030 

1.5030 

302 

1.5323 

1.5323 

30 

1.4952 

1.4951 

297 

1.5321 

1.5321 

25 

1.4809 

1.4805 

289 

1.5317 

1.5317 

21 

1.4625 

1.4627 

285 

1.5315 

1.5315 

19 

1.4415 

1.4410 

277 

1.5312 

1.5312 

17 

1.4152 

1.4148 

271 

1.5310 

1.5310 

15 

1.3736 

1.3735 

263 

1.5307 

1.5306 

13 

1.3407 

1.3403 

68  LIGHT 

second,  and  therefore  none  at  all.  In  the  final  lecture  of 
this  course  we  shall  deal  with  some  relations  between  light 
and  electricity,  the  connection  between  which,  according 
to  modern  views,  is  most  intimate.  Then  we  shall  be  in  a 
better  position  to  understand  that  when  there  are  no  vi- 
brations, so  that  you  have  a  steady  electric  field,  the  square 
of  the  refractive  index  must  be  identified  with  what  has 
long  been  known  as  the  specific  inductive  capacity  of  the 
material.  This  quantity  K  can  be  determined  by  suitable 
electrical  measurements,  and  when  the  value  so  obtained 
is  compared  with  that  derived  as  indicated  above  from  our 
formula,  there  is  an  excellent  agreement  between  the  two 
measures. 

Just  one  more  point  and  I  have  done.  I  have  said  that 
the  formula  gives  the  refractive  indices  for  frequencies  (/), 
which  are  not  very  close  to  any  of  the  natural  frequencies 
(/!  and  /2...)-  If  /  be  close  to/x  or  /2,  there  will  be  con- 
siderable absorption,  and  the  formula  must  be  modified. 
Instead  of  troubling  you  with  symbols,  I  shall  indicate  by  a 
figure  the  nature  of  the  change  that  occurs  in  the  neigh- 
borhood of  an  absorption  band.  Let  us  represent  fre- 
quencies (/)  by  distances  measured  along  the  horizontal 
line  CDF...  in  Fig.  10,  and  the  corresponding  refractive 
indices  (n)  by  distances  measured  at  right  angles  to  this 
line.  The  dotted  curve  in  the  figure  indicates  how  the  re- 
fractive index  varies  with  the  frequency,  when  we  are  not 
near  one  of  the  natural  frequencies.  You  will  observe  that 
the  curve  rises  steadily  to  the  right,  indicating  that  the  re- 
fractive index  increases  with  the  frequency ;  orange  is  more 
refracted  than  red,  and  blue  more  than  orange.  Next,  sup- 
pose that  we  are  dealing  with  a  substance  that  has  a  natu- 
ral frequency  at  D.  Then  our  theory  would  lead  to  a  formula 


DISPERSION  AND  ABSORPTION 


69 


connecting  n  and  /,  which  is  graphically  represented  by 
the  continuous  line  of  the  figure.  You  will  notice  a  strik- 
ing contrast  to  the  previous  case.  The  refractive  index 
no  longer  rises  steadily  as  the  frequency  increases.  As  the 


FIG.  10 

natural  frequency  is  approached,  the  refractive  index  rises 
abnormally,  and  it  begins  to  fall  and  to  fall  rapidly  when 
the  natural  frequency  is  passed.  In  the  special  case  that  I 
have  chosen,  orange  is  more  refracted  than  either  red  or 
blue,  and  blue  is  even  less  refracted  than  red.  The  order  of 
the  colors  in  the  spectrum  is  thus  quite  different  from  the 
ordinary,  and  it  appeared  so  lawless  when  first  observed, 
that  the  phenomenon  was  branded  with  the  name  anoma- 
lous dispersion.  We  now  see  that  there  is  nothing  lawless 
about  it,  and  that  the  same  theory  that  enables  us  to  ex- 
plain ordinary  or  normal  dispersion  gives  us  also  the  law 
(of  course  a  different  law)  for  this  apparent  anomaly. 


IV 

SPECTROSCOPY 

IN  the  last  lecture  we  were  occupied  a  good  deal  with 
discussions  as  to  the  structure  of  an  atom  and  a  molecule. 
We  saw  that,  according  to  the  most  recent  speculations, 
an  atom  is  no  longer  regarded  as  a  hard,  rigid  mass,  but  as 
a  throbbing,  palpitating  mechanism,  almost  a  living  thing. 
Such  a  mechanism  is  capable  of  vibrating  in  various  dif- 
ferent modes,  each  with  its  natural  frequency.  In  any 
given  substance  in  a  given  physical  condition,  the  num- 
ber of  the  possible  modes  of  vibration  and  the  values  of 
the  corresponding  frequencies  must  be  perfectly  definite. 
Any  periodic  movement  in  the  atom  or  the  molecule  will 
tend  to  set  up  disturbances  in  the  ether,  and  these  will 
be  periodic  and  have  the  same  frequencies  as  those  of  the 
vibrations  that  originate  them.  Whether  such  vibrations 
set  up  in  the  ether  will  produce  the  sensation  of  light  or 
not,  will  depend  on  their  frequency.  In  round  numbers 
this  frequency  must  lie  between  four  hundred  and  eight 
hundred  million  million  per  second,  as  vibrations  that  are 
either  slower  or  faster  than  this  do  not  affect  our  sight, 
although  their  influence  may  easily  be  detected  in  other 
ways.  Let  us  suppose,  for  example,  that  under  any  given 
circumstances  the  molecule  is  so  constructed  that  it  can 
vibrate  in  two  different  ways,  with  frequencies  of  five  hun- 
dred and  six  hundred  million  million  respectively.  These 
vibrations  will  set  up  light  of  two  different  colors,  and 

70 


SPECTROSCOPY  71 

if  the  substance  be  viewed  through  a  circular  hole  (as 
in  Newton's  experiment  referred  to  on  p.  15)  and  the  light 
passed  through  a  prism,  we  shall  see  two  circular  colored 
patches  in  different  positions,  one  of  them  blue  and  the 
other  orange.  If  the  diameter  of  each  patch  be  very 
small,  it  may  be  possible  to  distinguish  the  two  patches 
easily  and  clearly;  but  if  the  two  frequencies  be  chosen 
more  closely  together,  the  circular  patches  will  almost 
inevitably  overlap,  and  it  will  be  difficult  to  distinguish 
clearly  between  the  two.  This  overlapping  of  the  different 
colors  would  prove  a  very  serious  defect  if  accurate  measure- 
ments were  aimed  at,  and,  had  it  not  been  possible  to 
remove  the  defect,  the  modern  science  of  spectroscopy 
would  have  been  impossible.  The  simplicity  of  the  change 
required  in  Newton's  arrangement  is  a  striking  example 
of  the  occasional  importance  of  small  things  for  achieve- 
ment in  science.  All  that  is  needed  is  to  replace  the  circular 
hole  by  a  narrow  slit  parallel  to  the  sharp  edge  of  the  prism. 
Then,  instead  of  two  circular  patches  of  light  on  the  screen, 
we  have  two  narrow  lines  parallel  to  one  another,  and  unless 
the  two  frequencies  be  nearly  coincident,  these  lines  will 
be  clearly  distinguished  and  their  positions  easily  deter- 
mined with  precision  and  accuracy. 

To  understand  the  principles  of  spectroscopy,  you  must 
bear  in  mind  that  different  lines  in  the  spectrum  indicate 
different  frequencies,  and  each  frequency  corresponds  (as 
a  rule)  to  a  different  mode  of  vibration.  Of  course  much 
may  be  going  on  within  the  molecule  that  does  not  influence 
our  sight  (as  we  have  seen,  the  range  of  sensitiveness  of 
the  eye  is  limited),  and  again  it  may  require  a  stimulus  of  a 
special  kind,  such  as  a  high  temperature,  to  set  any  particu- 
lar mode  of  vibration  in  action.  Thus  a  substance  may  be 


72  LIGHT 

vibrating  in  many  modes,  with  frequencies  too  high  or  too 
low  for  us  to  see,  and  we  may  at  one  time  observe  lines  in 
the  spectrum  of  an  element  which  are  not  visible  at  all 
under  different  circumstances.  The  important  point  for 


violet       indigo  blue    green  yellow  orange 


Lithium 


Calcium 


Strontium 
FIG.  11 

us  at  present  is  that,  if  we  are  right  in  regarding  a  substance 
as  vibrating  with  definite  natural  frequencies,  we  should 
expect  that  its  spectrum,  viewed  under  proper  conditions, 
would  not  be  a  continuous  band  of  color,  but  a  series  of 
isolated  bright  lines,  each  of  a  color  corresponding  to  the 
frequency.  And  as  a  matter  of  fact  this  is  so,  as  you  will 
see  from  the  experiment  to  be  made  immediately,  or  from 
Fig.  11,  which  indicates  the  position  and  color  of  the  bright 
lines  in  the  emission  spectra  of  various  elements.  It  is 
important  to  observe  that  these  all  represent  the  spectra 
of  elements  that  are  in  the  form  of  gas  or  vapor.  If  the 
substance  is  in  the  solid  or  liquid  state,  its  spectrum  no 
longer  consists  of  a  series  of  isolated  bright  lines,  but  is 
continuous.  This  difference  in  the  aspect  of  the  spectrum 


SPECTROSCOPY  73 

of  a  substance  —  gaseous  in  one  case,  liquid  or  solid  in  the 
other  —  is  of  fundamental  importance  in  the  theory  of 
spectroscopy,  and  it  may  be  well  to  get  a  glimpse  of  the 
reason  for  the  difference.  According  to  the  generally 
accepted  view  as  to  the  nature  of  a  gas,  the  molecules  of 
such  a  substance  are  in  constant  motion.  Collisions  be- 
tween neighbors  are  therefore  to  be  expected,  the  frequency 
of  these  collisions  depending,  amongst  other  things,  on  the 
distance  between  the  neighbors,  or  on  the  density  of 
the  population.  If  the  gas  be  not  very  much  compressed, 
the  distance  between  neighboring  molecules  will  be  large 
enough  to  allow  them  "to  move  fairly  freely  and  to  execute 
their  natural  vibrations  without  being  disturbed  by  con- 
stant collisions.  Suppose,  however,  that  the  gas  is  com- 
pressed enough  to  liquefy  it,  or  that  further  changes 
are  made  until  a  solid  is  obtained.  Clearly  the  condi- 
tions of  the  molecules  have  been  greatly  modified.  In- 
stead of  being  fairly  free  to  move,  each  is  now  cabined, 
cribbed,  and  confined  and,  as  a  consequence,  collisions  be- 
tween neighboring  molecules  are  almost  constantly  taking 
place.  Thus,  instead  of  a  few  definite  modes  of  vibration,  we 
have  vibrations  of  almost  every  possible  frequency,  and  the 
spectrum  is  continuous.  Here  in  this  electric  arc  you  have 
a  solid  hot  enough  to  send  out  a  brilliant  light.  Pass  the 
light  through  the  prism  to  analyze  it,  and  you  see  a  brilliant 
spectrum  on  the  screen.  You  observe  that  it  is  perfectly 
continuous,  no  sign  of  a  break  or  an  isolated  patch  of  bright- 
ness as  your  eye  passes  from  red  to  violet,  through  all  the 
familiar  colors  of  the  rainbow.  Now  place  a  piece  of  so- 
dium in  the  arc.  The  heat  is  intense  enough  to  turn  it 
instantly  into  vapor,  and  you  see  at  once,  in  addition  to 
what  was  seen  before,  a  bright  line  in  the  orange.  The 


74  LIGHT 

solid  carbon  pencil  gives  a  continuous  spectrum,  the  gaseous 
sodium  an  isolated  line  or  series  of  lines. 

You  have  seen,  then,  that  a  substance  in  the  form  of 
a  vapor  or  gas  will,  if  viewed  under  proper  conditions, 
exhibit  a  spectrum  crossed  by  certain  bright  lines.  The 
science  of  spectrum  analysis  rests,  in  the  main,  on  two  facts 
with  reference  to  these  lines.  In  the  first  place,  the  position 
of  the  lines  is  always  the  same  for  the  same  element  in  the  same 
condition,  and  in  the  second  place,  the  arrangement  of  the 
lines  is  different  for  different  elements.  Once  this  is  grasped, 
there  can  be  no  difficulty  in  understanding  how  the  study 
of  spectra  enables  us  to  detect  the  chemical  nature  and  the 
condition  of  various  substances,  whether  they  be  in  our 
laboratories,  or  in  the  Sun,  over  ninety  million  miles  away, 
or  in  some  star  away  in  the  measureless  abyss  of  space. 

For  purposes  of  investigation,  we  need  an  instrument  that 
will  enable  us  to  see  these  bright  lines  clearly  and  measure 
their  relative  positions  accurately.  An  instrument  specially 
designed  for  this  purpose  is  called  a  spectroscope.  It  is  a 
wonderful  instrument,  for,  although  constructed  on  the 
simplest  principles,  it  has  revolutionized  astronomy  and 
done  great  things  for  chemistry  and  physics.  We  want 
some  means  of  separating  the  light  that  arises  from  the 
different  natural  vibrations  with  different  frequencies ;  in 
other  words,  we  want  dispersion.  The  simplest  instrument 
for  producing  this  is  that  employed  to  such  good  purpose 
by  Newton,  the  prism.  Figure  12  shows  four  such  prisms 
(P)  mounted  between  two  telescopes,  A  and  B,  so  as  to 
make  a  spectroscope  of  the  simplest  type.  The  light  from 
the  substance  to  be  examined  passes  through  a  narrow  slit 
into  telescope  A,  and  after  being  bent  and  dispersed  by 
the  prisms,  it  enters  telescope  B,  and  impresses  itself  on 


SPECTROSCOPY  75 

an  eye  looking  through  this  telescope.  The  instrument 
may  have  only  a  single  prism,  but  this  will  not  produce 
great  dispersion,  and  may  not  separate  the  various  lines  as 
widely  as  is  desired.  To  increase  the  dispersion,  two  or  more 
prisms  are  employed,  the  light  passing  through  one  after 
another  and  being  more  dispersed  at  each  passage.  This 


FIG.  12 

arrangement  has  the  defect  that  a  considerable  amount  of 
light  is  lost  by  reflection  and  absorption,  and  the  loss  may 
be  so  great  that  the  fine  lines  are  not  clearly  visible.  To 
avoid  this  serious  defect,  the  more  modern  spectroscopes 
employ  another  means  of  producing  large  dispersion.  The 
prism  is  replaced  by  a  grating,  a  contrivance  for  dispersing 
light,  the  principle  of  which  will  be  dealt  with  in  a  later 
lecture  on  diffraction.  Two  distinct  forms  of  grating  have 
been  invented.  The  first  was  made  by  ruling  a  series  of  fine 
lines  on  glass  or  speculum,  and  was  perfected  by  Rowland 
of  Baltimore ;  the  second,  the  echelon  spectroscope,  due  to 
Michelson  of  Chicago,  consists  of  a  series  of  thin  glass 


76  LIGHT 

plates  piled  on  one  another  like  a  flight  of  steps.  To  a 
spectroscope  of  any  of  these  forms  a  photographic  apparatus 
may  be  attached  so  as  to  obtain  a  permanent  record  on 
a  plate  instead  of  a  passing  impression  on  the  eye.  Such 
an  arrangement  is  called  a  spectrograph,  and  it  is  one  of  the 
most  important  instruments  in  an.astrophysical  observa- 
tory. 

On  looking  through  a  spectroscope  at  a  luminous  object, 
you  see  its  spectrum.  If  the  spectrum  be  continuous,  you 
know  that  you  are  looking  at  a  solid  or  a  liquid  hot  enough 
to  emit  light;  whereas,  if  the  spectrum  be  discontinuous, 
you  are  looking  at  a  gas.  Thus  a  mere  glance  through  a 
spectroscope  enables  you  to  tell  in  a  moment  something 
of  the  physical  condition  of  an  object,  and  this  whether 
the  object  be  near  or  far.  In  this  way  we  know  that 
comets  are  mainly  glowing  gas,  and  so  are  many  nebulse. 
In  all  the  wonders  of  the  heavens,  few  things  are  so  impress- 
ive as  the  gigantic  cloudlike  forms,  such  as  the  great  nebula 
in  Orion.  Is  each  of  these  a  vast  collection  of  stars  like  the 
Milky  Way,  or  is  its  structure  quite  different  from  this? 
After  much  difference  of  opinion  among  astronomers,  the 
question  was  finally  settled  by  Sir  William  Huggins,  one  of 
the  pioneers  of  spectroscopy.  "  On  the  evening  of  August 
29,  1864,"  he  says,  "I  directed  the  spectroscope  for  the 
first  time  to  a  planetary  nebula  in  Draco.  I  looked  into 
the  spectroscope.  No  spectrum  such  as  I  had  expected ! 
A  single  bright  line  only !  .  .  .  A  little  closer  looking 
showed  two  other  bright  lines  on  the  side  towards  the  blue, 
all  three  lines  being  separated  by  intervals  relatively  dark. 
The  riddle  of  the  nebulae  was  solved.  The  answer  which 
had  come  to  us  in  the  light  itself  read :  Not  an  aggregation 
of  stars,  but  a  luminous  gas" 


SPECTROSCOPY  77 

Thus  the  spectroscope  tells  us  something  of  the  physical 
condition  of  a  substance.  It  shows  whether  it  is  gaseous 
or  not.  But  it  does  much  more  than  this;  it  reveals  the 
chemical  constitution.  This  is  settled  by  noting  carefully 
the  positions  of  the  various  lines  in  the  spectra,  and  com- 
paring them  with  the  positions  of  lines  in  the  spectra  of 
known  elements.  A  glance  at  Fig.  11  will  serve  to  recall 
the  fact  that  the  spectra  of  no  two  different  elements  are 
the  same,  so  that  if  we  see  in  the  spectrum  of  any  substance 
the  characteristic  lines  of  any  element,  e.g.  hydrogen,  we 
can  be  certain  that  the  substance  contains  hydrogen.  A 
more  careful  examination  of  the  various  spectra  makes  it 
evident  that  the  chance  of  confusing  two  elements  is 
extremely  small.  We  now  possess  very  carefully  made 
maps  of  the  spectra  of  the  elements,  and  these  greatly 
facilitate  the  process  of  identification.  This  spectroscopic 
method  of  examining  the  chemical  constitution  of  a  sub- 
stance is  a  very  simple  and  a  very  valuable  one.  Its  extreme 
delicacy  enables  us  to  detect  the  presence  of  minute  quan- 
tities of  a  substance  that  no  ordinary  chemical  process  could 
possibly  detect.  Morever,  the  fact  that  a  different  series  of 
lines  in  the  spectrum  indicates  a  different  element  shows  that 
if  we  find  spectra  differing  from  any  already  known,  we  have 
good  ground  for  supposing  that  we  are  in  the  presence  of 
a  new  element.  And  so  it  happened  that  one  of  the  first 
fruits  of  the  science  of  spectroscopy  was  the  discovery  of 
new  elements.  Bunsen  was  the  pioneer  in  this  field.  In 
1860  he  discovered  in  this  way  the  elements  C cesium  and 
Rubidium;  in  the  following  year  Crookes  discovered 
Thallium,  and  there  has  been  a  long  list  of  similar  dis- 
coveries since  then. 

This  spectroscopic  method  of  distinguishing  one  substance 


78  LIGHT 

from  another  by  the  positions  of  the  lines  in  their  spectra 
has,  during  the  last  half  century,  become  one  of  the  common- 
places of  chemistry.  In  recent  years,  however,  the  attention 
of  physicists  has  been  directed  to  other  features  of  the  lines 
than  their  mere  positions.  Even  a  slight  examination  reveals 
the  fact  that  there  are  various  differences  between  the  lines, 
e.g.  one  is  much  broader,  or  much  brighter,  than  another. 
In  these  latter  days  each  line  is  subjected  to  the  most  minute 
examination,  the  pioneer  in  this  field  of  investigation  hav- 
ing been  Michelson  of  Chicago.  By  means  of  an  ingen- 
ious instrument  of  his  own  invention,  —  the  interferometer, 
an  instrument  the  explanation  of  which  depends  on  the 
principle  of  interference  that  is  dealt  with  in  a  later  lecture, 
—  he  observes  certain  features  of  the  lines,  and  records  the 
results  of  his  observations  graphically  in  the  form  of  what 
he  calls  visibility  curves.  If  you  look  at  those  curves  for 
different  substances,  you  will  see  that  one  line  differs  very 
markedly  from  another.  Here,  for  example,  in  Fig.  13, 
are  the  curves  for  different  lines  in  the  spectra  of  various 
substances:  (a)  for  the  red  line  of  cadmium,  (6)  the  red 
line  of  hydrogen,  and  (c)  the  green  line  of  mercury.  From 
the  study  of  the  form  of  these  lines,  Michelson  makes 
various  interesting  and  important  deductions  as  to  the 
character  of  the  source  that  sends  out  the  light  radiation. 
He  concludes  that  (a)  comes  from  a  source  of  the  simplest 
possible  character,  a  single  vibrator  sending  out  waves 
that  are  almost  perfectly  homogeneous.  The  form  of  (&) 
seems  to  indicate  that  the  source  is  more  complex  than  with 
(a),  and  Michelson  concluded  that  the  radiation  came  from 
two  sources,  differing  ve1  y  slightly  in  frequency  and  in  in- 
tensity. His  prediction  as  to  the  essentially  double  char- 
acter of  this  line  was  afterwards  confirmed  by  direct  obser- 


SPECTROSCOPY 


79 


vation.  The  curve  (c)  reveals  a  much  more  complex  source ; 
in  this  case,  apparently,  the  radiation  comes  from  a  number 
of  vibrators  differing  both  in  frequency  and  in  intensity. 
The  interest  of  such  investigations  centers  entirely  on  the 
light  that  it  sheds  on  the  fundamental  problem  of  the  struc- 


(b) 


(c) 


FIG.  13 


ture  of  the  atom,  as  the  vibrations  must  be  due  to  motion 
within  that  small  kingdom. 

Thus  far  we  have  spoken  only  of  the  positions  and  fea- 
tures of  certain  bright  lines  in  the  spectrum,  these  bright 
lines  being  separated  by  spaces  that  are  relatively  dark. 
On  looking  at  the  solar  spectrum  with  a  good  spectroscope, 
a  different  phenomenon  is  revealed.  The  spectrum  is  seen 
to  be  bright  and  all  but  continuous  except  that  it  is  crossed 
by  a  large  number  of  fine  dark  lines.  These  lines  were 


80  LIGHT 

first  carefully  observed  by  Fraunhofer  in  1814,  and  are 
still  known  by  his  name.  In  the  intervening  century  they 
have  been  studied  with  the  greatest  care,  and  the  task  of 
mapping  them  accurately  has  been  undertaken  and  carried 
out  with  marvellous  patience  and  skill.  Thus  Rowland's 
map  records  the  places  of  about  tweny  thousand  of  these 
lines.  What  is  their  meaning,  and  why  should  we  trouble 
to  record  their  positions  with  so  much  care?  After  the 
last  lecture  on  absorption,  we  should  have  no  difficulty 
in  answering  such  questions.  A  vibrating  system  absorbs 
the  energy  of  waves  that  have  the  same  frequencies  as  the 
natural  frequencies  of  the  system.  Look  at  the  spectrum 
of  the  vapor  of  sodium.  You  will  see  two  bright  lines  (D) 
close  to  one  another  in  the  orange,  and  the  positions  of  these 
lines  depend  upon  the  frequencies  of  the  natural  vibrations 
of  the  sodium  atom.  If  now  a  train  of  waves  passes  through 
the  sodium  vapor,  those  waves  will  have  their  energy 
extracted  that  have  frequencies  corresponding  exactly  to 
those  of  these  two  D  lines.  Hence,  if  the  light  that  falls 
upon  the  sodium  vapor  come,  let  us  say,  from  a  glowing 
liquid  hotter  than  this  sodium,  the  continuous  spectrum 
of  the  liquid  will  be  crossed  by  two  dark  lines  coinciding 
in  position  with  those  D  lines.  This  is  the  phenomenon 
of  reversal.  It  is  no  mere  deduction  from  theory,  but  a  fact, 
verified,  as  you  see,  by  the  experiment  that  is  being  con- 
ducted before  you.  The  principle  involved  in  the  ex- 
planation here  given  had  occurred  to  Stokes  and  other 
physicists  in  the  first  half  of  last  century ;  but  it  was  re- 
served for  Kirchhoff  in  1859  to  set  it  forth  clearly  and  test 
it  by  experiment.  From  that  date  we  may  mark  the  rise 
of  what  is  often  called  the  new  astronomy  —  an  applica- 
tion of  spectroscopic  methods  to  the  study  of  the  physi- 


SPECTROSCOPY 


81 


cal  condition  of  the  heavenly  bodies  which  has  led  to  many 
epoch-making  results. 

In  Fig.  14  the  phenomenon  of  reversal  is  exhibited  by 
showing  side  by  side  the  bright  lines  of  the  emission  spec- 
tra, and  the  dark  lines  in  the  absorption  spectra  of  a  few 
elements.  The  point  to  be  specially  noticed  is  the  coinci- 


Sodium 


dence  in  position  of  the  bright  lines  in  one  case  with  the  dark 
lines  in  the  other.  It  may  at  first  be  thought  that  these 
coincidences  are  only  accidental.  This  might,  indeed,  be 
so  were  there  only  a  few  coincidences,  but  the  number  ac- 
tually observed  puts  the  idea  of  chance  out  of  the  question. 
Thus,  in  the  case  of  the  iron  lines,  Kirchhoff,  on  taking  into 
account  the  number  of  the  lines,  their  distances  from  one 
another,  and  the  degree  of  exactness  with  which  their  posi- 
tions could  be  determined,  calculated  that  the  odds  were 
at  least  a  million  million  million  to  one  against  a  mere 
chance  coincidence.  We  may  thus  feel  practically  certain 
that,  when  we  see  dark  lines  in  a  spectrum  coinciding  in 


82  LIGHT 

position  with  bright  lines  in  the  emission  spectrum  of  an 
element,  we  are  looking  at  the  light  from  a  hot  source 
shining  through  a  cooler  vapor  containing  the  element 
in  question.  It  will  be  realized  at  once  that  this  enables 
us  to  detect  the  presence  of  elements  in  any  body,  be  it  near 
or  far,  that  is  in  a  certain  physical  condition.  What  this 
condition  is  should  be  carefully  borne  in  mind.  The  body 
must  be  hot  enough  to  give  a  continuous  spectrum,  and  it 
must  be  surrounded  by  a  cooler  atmosphere.  The  spectro- 
scope then  enables  us  to  determine  the  ingredients  of  this 
atmosphere.  Naturally,  the  method  was  first  tried  upon  the 
Sun,  and  the  observation  of  the  Fraunhofer  lines  and  the 
comparison  of  their  positions  with  those  of  the  bright  lines 
in  the  spectra  of  various  elements  have  made  a  great  ad- 
vance in  our  knowledge  of  solar  chemistry  possible  and 
easy.  In  this  way  a  very  large  number  of  familiar  elements 
have  been  discovered  in  the  Sun,  so  many  that  it  may  be 
simpler  to  mention  a  few  that  have  not  been  found  there, 
such  as  gold,  arsenic,  mercury,  nitrogen,  and  sulphur. 
There  are  still  a  great  many  unidentified  lines  in  the  solar 
spectrum,  some  twelve  thousand  having  been  registered  that 
are  as  yet  without  chemical  interpretation.  Clearly,  the 
method  here  sketched  is  not  confined  to  the  Sun  but  is  ap- 
plicable to  any  body  whose  spectrum  can  be  examined. 
Thus,  for  example,  we  now  know  with  certainty  that  many 
of  the  stars  are  made  up  of  much  the  same  material  as  our 
earth,  and  that  they  are  in  much  the  same  condition  as  the 
Sun,  that  is,  they  are  hot  bodies  surrounded  by  a  gaseous 
atmosphere. 

Turning,  for  a  moment,  from  stellar  chemistry  to  more 
mundane  matters,  we  may  observe  that  the  careful  study 
of  absorption  spectra  may  yet  help  us  to  solve  many  funda- 


SPECTROSCOPY  83 

mental  problems  in  molecular  physics  and  chemistry.  In 
this  field  much  useful  work  has  already  been  done  by 
Hartley  and  others  in  the  examination  of  the  absorption 
spectra  of  various  organic  compounds.  These  compounds 
are  formed  by  grouping  different  elements  round  a  carbon 
atom,  and  a  fundamental  question  is :  How  are  the  atoms 
arranged  ?  if  you  could  see  them,  what  would  be  their  rela- 
tions to  one  another  in  space  ?  Such  questions  can  some- 
times be  answered,  with  more  or  less  assurance,  by  the  care- 
ful study  of  the  nature  of  the  chemical  reactions  of  the 
substance  under  different  circumstances.  But  often  this 
method  fails,  and  Hartley  shows  that  the  study  of  absorp- 
tion spectra  may  help  us  out  of  the  difficulties,  and  enable 
us  to  say,  for  example, 

that  in   a  certain   com-     A— — ~ # 

pound  the  hydrogen  atom       "J"v 

is  linked  to  the  nitrogen 

and  not  to  the  oxygen.    A  mere  change  of  linkage,  that 

is,  a  change  of  grouping,  can  modify  the  spectrum,  and  the 

study  of  such  changes  bids  fair  to  give  us  an  insight  into 

the  actual  arrangement  of  atoms  in  the  group. 

In  dealing  with  so  extensive  a  subject  as  spectroscopy 
in  a  lecture  such  as  this,  it  must  soon  be  realized  that  there 
is  not  sufficient  time  to  do  more  than  speak  of  its  funda- 
mental principles  and  point  out  a  few  of  its  most  striking 
achievements.  Some  of  the  latter  have  already  been  in- 
dicated ;  let  us  glance  at  a  few  more.  Spectroscopy  enables 
us  to  discover  not  only  the  physical  condition  and  chemical 
nature  of  various  heavenly  bodies,  but  also,  in  certain  circum- 
stances, the  speed  at  which  they  are  moving.  To  understand 
this,  suppose  that  you  are  sitting  in  a  canoe  at  A  (Fig.  15),  and 
that  you  set  up  a  series  of  waves  by  dipping  your  paddle 


84  LIGHT 

into  the  water  once  a  second.  If  V  be  the  speed  with  which 
the  waves  move  over  the  surface  of  the  water,  the  first  wave 

will  reach  B  at  a  time  ,  and  the  second  at  a  time  1-f 
-  ,  both  times  being  measured  in  seconds  from  the  mo- 
ment when  your  paddle  first  touched  the  water  at  A.  The 
interval  of  time  between  the  two  waves  reaching  B  is  one 
second.  This  will  be  the  case  whatever  be  the  velocity 
V,  so  that  a  change  of  velocity  does  not  affect  the  time  in- 
terval between  the  waves  that  strike  upon  B]  in  other 
words,  it  does  not  affect  the  frequency  of  the  oscillations  at 
B.  But  now  suppose  that  you  paddle  your  canoe  toward  B 
with  velocity  v.  The  first  wave  reaches  B  at  the  time 

—  as  before.    The  second  wave  again  starts  one  second 

later,  but  it  has  not  so  far  to  go  in  reaching  B.  It  goes  only 
the  distance  CB  =  AB  —  v,  so  that  it  arrives  at  B  at  the 

,.  (AB  —  v)       AB  ,  -      v      r™     .  ,        ,    -  .. 

time  1  +  — — y — -      -y-  +  1  —  y.    The  interval  of  time 

between  the  first  and  second  waves  that  reach  B  is  thus 
changed  from  1  to  1  —  —  (and  it  would  be  easy  to  show  in  a 
similar  way  that  the  interval  would  be  changed  to  1  +  ^  if 

you  paddled  in  a  direction  away  from  B  instead  of  towards  it). 
This  change  of  interval  means,  of  course,  a  change  of  fre- 
quency in  the  oscillations  observed  at  B.  You  will  see  that 
there  is  nothing  in  the  argument  that  limits  its  application 
to  water  waves ;  if  true  at  all,  it  should  apply  equally  to 
waves  in  water,  or  any  other  medium,  such  as  air  or  ether. 
The  only  difficulty  in  its  application  to  light  is  that  a  care- 
ful scrutiny  reveals  some  rather  delicate  questions  as  to  the 


SPECTROSCOPY  85 

relative  motion  of  ether  and  matter,  questions  that  it  would 
be  out  of  place  to  discuss  on  this  occasion.  The  principle 
itself  was  first  clearly  stated  by  Doppler  in  1843,  and  was 
tested  two  years  later  by  observations  on  sound  from  loco- 
motives. The  theory  of  sound  shows  that  the  pitch  of  a 
note  depends  on  the  frequency  of  the  oscillations  in  the  air 
that  strikes  upon  the  ear.  Hence,  according  to  Doppler's 
principle,  the  pitch  of  a  note  should  change  in  a  definite 
way,  as  the  source  of  sound  approaches  and  recedes  from 
an  observer.  The  general  character  of  the  change  can  be 
observed  by  any  one  who  cares  to  listen  carefully  to  the 
sound  of  the  bell  when  a  bicycle  passes  him  in  the  street. 
The  object  of  the  experiments  referred  to  was  to  test  the 
principle  in  a  more  thorough  fashion  by  exact*  measure- 
ments of  the  pitch,  and  the  results  showed  clearly  that  the 
principle  was  well  grounded  in  fact. 

To  understand  the  application  of  Doppler's  principle 
to  spectroscopy,  you  have  only  to  recall  the  fact  that  the 
positions  of  the  lines  in  the  spectrum  depend  upon  the  fre- 
quency of  the  vibrations.  Consequently,  a  change  of  fre- 
quency should  reveal  itself  by  a  shift  in  the  positions  of  the 
spectral  lines,  and  a  measurement  of  this  shift  gives  us  the 
means  of  calculating  the  velocity  of  the  source  of  light  (say 
a  star),  or  rather  the  component  of  its  velocity  in  the  direc- 
tion of  the  line  of  sight.  Many  interesting  results  have  been 
obtained  by  this  mode  of  research.  Thus,  for  example,  it 
has  enabled  us  to  estimate  the  speed  of  different  parts  of 
the  Sun,  such  as  the  mighty  currents  of  gas  in  the  neigh- 
borhood of  a  Sun  spot,  or  those  awe-inspiring  tongues  of 
flame  (the  prominences)  that  shoot  up  from  the  central 
fire  of  the  Sun,  in  some  cases  at  the  rate  of  about  seven 
hundred  miles  per  second.  Similarly,  it  has  made  it  pos- 


86  LIGHT 

sible  to  determine  the  speed  of  many  stars  that  are  far  too 
distant  to  have  their  velocities  gauged  by  any  other  method. 
As  is  to  be  expected,  the  velocities  are  found  to  be  very 
different  for  different  stars.  Some  are  moving  relatively 
to  the  Sun  at  about  one  mile  per  second,  others  at  nearly 
a  hundred  miles.  The  majority  on  one  side  of  the  heavens 
have  a  general  relative  motion  towards  the  Sun,  those  on  the 
opposite  side  a  similar  motion  away  from  the  Sun.  The 
inference,  of  course,  is  that  the  Sun  itself  is  not  stationary, 
but  is  sweeping  through  space  with  his  attendant  train  of 
planets.  Another  interesting  achievement  of  this  mode  of 
research  is  that  it  has  enabled  us  in  many  cases,  in  a  sense, 
to  see  that  which  is  invisible.  In  general,  no  star  can  be 
seen  unless  it  be  hot  enough  to  emit  light,  and  yet,  though 
unseen,  its  presence  may  be  none  the  less  distinctly  felt. 
Whether  hot  or  cold,  it  will  still  have  weight,  and  will  have 
the  mystic  power  of  gravitation,  of  attracting  all  neighbor- 
ing bodies  towards  itself.  If  heavy  enough,  it  will  compel 
its  neighbors  to  move  round  it  in  definite  orbits,  like  the 
planets  round  the  Sun.  If  we  see  a  star  moving  round  an 
orbit,  we  may  be  certain  that  it  has  a  companion  that 
attracts  it,  whether  this  companion  be  visible  or  not,  and 
the  principles  of  celestial  mechanics  may  enable  us  to  de- 
termine various  facts  about  this  dark  companion  —  for 
example,  its  weight.  Now  the  observation  of  the  shifting 
of  the  lines  in  the  spectrum  of  various  stars,  when  conducted 
over  a  long  period,  often  shows  that  the  stars  are  not  moving 
uniformly  in  a  definite  direction,  but  are  circling  round  an 
orbit,  and  so  from  the  knowledge  of  the  visible  we  are  led 
to  infer  the  presence  of  the  invisible.  The  application  of 
Doppler's  principle  also  occasionally  gives  us  information 
as  to  the  structure  of  the  heavenly  bodies.  Among  the 


SPECTROSCOPY  87 

most  striking  objects  to  be  seen  with  a  good  telescope  are 
the  beautiful  rings  of  Saturn.  What  is  the  structure  of 
these  rings?  This  was  a  question  long  debated,  until 
Maxwell  in  1859  showed  by  means  of  mechanical  principles 
that  the  rings  could  not  possibly  be  solid,  for  in  such  a 
state  they  would  be  unstable  and  would  fly  to  pieces.  The 
argument  convinced  all  those  who  were  not  afraid  of  the 
highroad  of  mathematics  and  mechanical  science,  but  it 
was  not  till  1895  that  we  had  ocular  demonstration  that 
Maxwell  was  right.  In  that  year  Keeler  showed,  by  a  care- 
ful study  of  the  spectra  of  the  light  reflected  from  the  rings, 
that  the  inner  edge  is  moving  faster  than  the  outer,  which 
of  course  would  be  impossible  with  a  solid.  As  Maxwell 
had  indicated,  the  ring  is  a  group  of  meteorites,  each  mov- 
ing as  a  separate  planet  round  Saturn  as  its  central  Sun. 

So  much  for  Doppler's  principle  and  its  applications; 
let  us  turn  to  some  other  phases  of  the  modern  science  of 
spectroscopy.  We  have  had  occasion  to  refer  to  the  solar 
prominences,  those  mighty  tongues  of  flame  that  shoot 
outwards  from  the  Sun  to  distances,  sometimes,  of  several 
hundred  thousand  miles.  Huge  and  brilliant  as  they  are, 
they  are  not  to  be  seen  under  ordinary  circumstances  with 
the  naked  eye,  for  their  brightness  is  overpowered  in  the  glare 
of  the  sunlight.  And  so,  until  forty  years  ago,  they  were 
thought  of  only  as  an  eclipse  phenomenon,  and  were  looked 
for  eagerly  on  those  rare  occasions  when  at  any  given  place 
the  Sun  is  seen  in  total  eclipse.  All  this  was  suddenly 
changed  by  an  epoch-making  application  of  the  spectroscope 
—  an  application  due  to  the  ingenuity  of  Janssen,  Lockyer, 
and  Huggins  by  means  of  which  the  prominences  may 
be  seen  on  any  day.  The  principle  of  the  arrangement  is 
very  simple.  A  spectroscope  disperses  the  sunlight  that 


88  LIGHT 

passes  through  it ;  it  spreads  out  the  image  of  the  narrow 
slit  from,  say,  one-thousandth  of  an  inch  to  many  feet. 
This  dispersion,  as  we  saw  in  an  earlier  lecture,  is  due 
entirely  to  the  different  refrangibility  of  the  various  con- 
stituents that  go  to  make  up  the  composite  thing  that  we 
call  sunlight.  Homogeneous  light,  light  of  a  definite  re- 
frangibility, is  not  dispersed.  Now  it  so  happens  that  the 
solar  prominences  are  made  up  mainly  of  homogeneous 
light,  such  as  the  light  from  hydrogen  or  helium  or  calcium. 
Consequently,  while  the  light  from  the  Sun  is  spread  out 
by  the  spectroscope,  that  from  the  prominence  is  not. 
Hence,  by  employing  a  spectroscope  of  sufficient  dispersive 
power,  it  is  possible  to  spread  out  the  sunlight  so  much  that 
the  prominence  looks  bright  in  comparison  with  the  Sun, 
and  may  be  plainly  seen  on  any  day  of  the  year,  without 
the  tedium  of  waiting  for  a  total  eclipse. 

That  was  an  ingenious  and  important  device;  but  even 
more  so  was  the  later  development  due  to  Hale  (now  of  the 
Mt.  Wilson  Solar  Observatory).  This  device  enables  us  not 
only  to  see  the  prominences  at  any  time,  but  to  photograph 
them,  and  thus  obtain  a  permanent  record  of  their  features. 
The  form  of  spectroscope  specially  designed  for  this  purpose 
is  known  as  a  spectroheliograph.  Let  us  see  how  it  works. 
A  special  feature  of  the  solar  prominences  is  the  presence 
therein  of  quantities  of  the  vapor  of  calcium,  the  spectrum 
of  which  is  characterized  by  two  bright  lines  called  H  and  K. 
Suppose  that  we  present  the  slit  of  the  spectroheliograph 
to  a  prominence,  so  as  to  allow  the  light  from  the  promi- 
nence to  stream  through  the  instrument.  In  this  way  we 
look,  as  through  a  narrow  window,  at  a  section  ABCD  (Fig. 
16).  The  light  from  this  section,  if  passed  through  a  prism 
or  other  dispersing  apparatus,  would  be  drawn  out  into  a 


SPECTROSCOPY 


spectrum,  and  if  you  were  to  put  your  eye  in  the  position 
of  the  line  K,  you  would  be  in  a  position  specially  favorable 
to  receive  impressions  from  light  that  came  from  the  vapor 
of  calcium.  As  this  vapor  is  an  important  ingredient  in  the 
prominence,  the  portion  BC  of  the  section  that  you  were 
observing,  would  appear  much  brighter  than  the  portions 
AB  and  CD  that  lay  outside  the  prominence.  In  this  way 
the  cross-section  BC 
of  the  prominence 
would  stand  out  more 
or  less  distinctly,  and 
by  moving  the  slit  up 
and  down,  you  could 
thus  observe  various 
cross-sections,  and  so 
map  out  the  whole 
prominence.  To  obtain 
a  permanent  record,  it 
is  necessary  to  replace 
the  eye  by  a  photographic  plate,  in  front  of  which  a  second 
slit  is  placed  in  such  a  position  that  it  catches  the  light 
from  calcium  vapor,  but  no  other  kind  of  light.  A  suit- 
able mechanism  moves  the  slits  so  as  to  give  a  succession 
of  photographs  corresponding  to  different  cross-sections  of 
the  prominence. 

The  method  here  sketched  was  first  tried  with  complete 
success  by  Hale  in  1892.  He  saw  at  once  that  it  could  be 
applied  to  the  study  of  other  solar  features.  If,  for  example, 
there  were  a  cloud  of  calcium  vapor  anywhere  in  the  Sun's 
surface,  the  same  method  would  enable  the  observer  to 
pick  it  out  and  photograph  it.  Hale  did  this  in  1892,  and 
his  more  recent  photographs  of  calcium  floccvli  reveal  the 


FIG.  16 


90  LIGHT 

fact  that  these  beautiful  clouds  are  specially  striking  in 
the  neighborhood  of  Sun  spots.  Then,  of  course,  there  is 
no  reason  to  confine  the  method  to  photographing  clouds 
of  calcium.  Other  elements  may  be  dealt  with  similarly. 
In  this  way,  working  with  one  of  the  hydrogen  lines,  Hale 
found  that  great  masses  of  this  gas  are  concentrated  in 
clouds  on  various  parts  of  the  Sun's  surface,  and  photo- 
graphs of  these  hydrogen  flocculi  show  them  to  be  so  nu- 
merous as  to  make  the  bright  face  of  the  Sun  present  a 
distinctly  mottled  appearance. 

We  have  seen  that  the  spectroscope  enables  us  to  detect 
the  presence  of  familiar  chemical  elements  in  the  Sun  and 
stars,  to  measure  the  velocities  of  such  distant  bodies,  and 
to  photograph  many  otherwise  invisible  features  on  the  face 
of  the  Sun.  We  have  also  seen  that  it  may  give  us  an  in- 
sight into  the  physical  condition  of  various  heavenly  bodies. 
A  continuous  spectrum  indicates  a  glowing  solid  or  liquid, 
while  a  discontinuous  spectrum  reveals  a  gas.  But  we  can 
often  tell  more  than  that  the  object  of  our  interest  is  a  great 
mass  of  gas.  We  may  learn  something  of  its  temperature 
and  of  its  pressure.  It  is  found  by  observation  that  the  rela- 
tive intensity  of  different  lines  varies  with  the  temperature 
of  the  source  of  light.  For  example,  in  the  spectrum  of 
magnesium,  there  are  two  lines,  a  and  6,  say;  of  these  two, 
a  is  brighter  than  b  at  the  temperature  of  the  electric  spark, 
but  b  is  brighter  than  a  at  lower  temperatures.  This  may 
serve  to  indicate  how  the  relative  intensity  of  the  lines  in 
the  spectrum  may  serve  as  a  clue  to  the  temperature  of 
the  glowing  gas.  Moreover,  the  character  of  the  spectral 
lines  is  altered  by  a  change  of  pressure.  If  the  pressure  be 
increased,  the  lines  broaden,  so  that  an  observation  of 
their  width  tells  us  something  of  the  pressure  of  the  gas, 


SPECTROSCOPY  91 

It  is  even  possible  to  take  a  photograph  (by  means  of  a 
spectroheliograph)  of  the  calcium  vapor  at1  the  base  of  the 
calcium  flocculi  in  the  Sun,  without  being  troubled  by  the 
lighter  vapor  above.  To  do  this,  it  is  merely  necessary  to 
set  the  second  slit  of  the  instrument  near  the  edge  of  the 
broad  K  bands,  so  that  the  light  from  the  rarer  vapor 
cannot  enter  the  spectroscope,  and  is  thus  debarred  from 
affecting  the  photographic  plate.  Such  a  device  has  made 
it  possible  to  learn  a  good  deal  of  the  structure  of  these 
flocculi,  by  examining  sections  of  them  taken  at  various 
levels. 

The  last  point  that  there  is  time  to  touch  upon  is  the 
contribution  that  spectroscopy  has  made  to  our  knowledge 
of  the  trend  of  stellar  evolution.  This  idea  of  development, 
or  evolution,  if  you  prefer  the  term,  has  become  a  common- 
place of  modern  thought  in  almost  every  field  of  speculation 
and  of  knowledge.  It  is  an  old  idea,  brought,  as  you  all 
know,  into  a  precise  form  that  immediately  appealed  to 
man's  imagination  by  Darwin  in  his  Origin  of  Species  — 
that  epoch-making  book  that  was  published  in  the  same 
year  in  which  Kirchhoff  laid  the  foundations  of  the  science 
of  spectroscopy.  Long  before  Darwin's  day,  the  idea  of 
stellar  evolution  had  been  broached,  the  idea  that  the 
heavenly  bodies  have  not  been  always  as  they  are  to-day, 
but  that  they  have  been  and  still  are  going  through  a  gradual 
process  of  change.  To  unravel  this  secret  of  the  universe 
and  get  some  insight  into  the  earlier  history  and  later 
destiny  of  the  worlds  around  us  is  one  of  the  grandest 
problems  that  the  pygmy  man  has  been  bold  enough  to 
attack.  Kant,  the  great  philosopher,  made  some  sugges- 
tive speculations,  and  Laplace,  the  great  mathematician, 
developed  them  into  a  definite  working  hypothesis.  But 


92  LIGHT 

all  such  thinking  was  somewhat  premature.  If  you  wish 
to  trace  the  development  of  anything,  you  must  know  as 
accurately  as  possible  its  physical  condition  at  various 
stages  of  its  growth.  People  are  naturally  somewhat 
skeptical  when  they  are  asked  to  believe  that  their  remote 
ancestors  were  probably  arboreal  in  their  habits ;  but  they 
are  really  not  in  a  position  to  judge  of  the  merits  of  such 
a  theory  unless  they  have  made  a  careful  study  of  the  dif- 
ferent stages  of  human  development.  And  so  with  the 
problem  of  stellar  evolution  it  is  necessary  to  begin  by 
rinding  out  all  that  can  be  known  of  the  actual  physi- 
cal condition  of  different  members  of  the  heavenly  host. 
Spectroscopy  is  making  the  solution  of  the  problem  possible ; 
it  cannot  be  said  to  have  solved  it  yet.  By  means  of  this 
science  we  now  know  a  good  deal  as  to  the  physical  condi- 
tions of  a  very  large  number  of  heavenly  bodies.  We  can 
thus  arrange  these  bodies  into  groups,  the  members  of  each 
group  having  certain  properties  in  common,  and  it  may  be 
that  these  groups  represent  different  stages  in  a  general  pro- 
cess of  development.  Suppose  we  put  them  into  six  groups, 
and  look  at  each  very  briefly.  First,  there  are  the  nebulae. 
Many  of  these  are  enormous  clouds  of  glowing  gas,  the 
bright  lines  in  their  spectra  indicating  the  presence  of 
hydrogen  and  helium,  and  of  an  unknown  element  which 
has  been  given  the  name  nebidum.  Out  of  these  cloud- 
like  masses  we  might  expect  various  forms  to  be  evolved, 
through  the  action  of  gravity  and  other  forces,  and  in  view 
of  certain  speculations  as  to  the  mode  of  their  evolution  it 
is  interesting  to  observe  that  of  120,000  nebulae  that  have 
been  examined,  more  than  half  have  a  spiral  form.  They 
look  like  mighty  Catherine  wheels  in  the  very  act  of  whirl- 
ing. Second,  we  have  the  special  class  of  nebula;  that  con- 


SPECTROSCOPY  93 

stitute  the  Orion  type.  Their  spectra  exhibit  no  bright 
lines  except  those  of  hydrogen  and  helium,  and  these  lines 
are  very  broad  and  faint.  Third  are  the  white  stars,  such 
as  Sirius.  Their  spectra  show  broader  lines  of  hydrogen, 
with  narrow  and  faint  dark  lines  of  iron,  sodium,  magnesium, 
and  a  few  other  elements.  Their  atmospheres  are  still  very 
rare,  much  rarer  than  that  of  the  Sun.  Fourth  come  the 
yellowish  stars  like  the  Sun.  They  have  far  more  dark  lines 
in  their  spectra  than  their  predecessors,  and  there  is  evidence 
of  much  greater  density.  Fifth,  we  have  the  red  stars,  of 
which  An  tares  is  a  type.  They  are  beginning  to  fade  into 
invisibility.  Their  spectra  are  much  more  complex  than 
those  of  the  previous  groups,  and  contain  a  great  many  lines, 
and  not  a  few  dark  bands  or  flu  tings.  Last  come  the  dark, 
invisible  stars.  They  are  too  cold  to  give  any  light,  and 
can  be  detected  only,  as  already  indicated,  by  the  shifting 
of  the  lines  in  the  spectrum  of  a  neighboring  bright  star. 

Here,  at  any  rate,  we  have  food  for  thought.  We  may 
feel  certain  that  some  process  of  development  is  in  prog- 
ress, for  nothing  that  we  know  well  stands  quite  still. 
But  what  is  the  exact  order  of  the  development,  whether 
that  order  is  everywhere  the  same,  and  whither  it  all 
tends  are  questions  we  may  hesitate  to  answer.  Here, 
probably  the  better  part  of  valor  is  discretion.  Later 
researches  have  revealed  many  difficulties  in  Darwin's 
theories,  and  put  many  a  stumbling-block  in  the  path  of 
him  who  is  too  eager  to  embrace  the  nebular  hypothesis 
of  Kant  and  Laplace  as  to  the  mode  of  stellar  evolution. 
The  leaders  of  thought  in  this  field  must  work  with  patience 
and  endurance  perhaps  for  many  a  generation  before  there 
is  anything  like  a  final  concord  in  answering  these  great 
questions.  I  leave  them  with  you  as  food  for  speculation 


94  LIGHT 

and,  if  vastness  attracts  you,  here  you  have  some  problems 
preeminently  to  your  taste.  You  are  not  asked  to  decipher 
the  history  of  man,  nor  to  tell  the  tale  of  the  "solid"  earth, 
which  is  the  scene  of  all  his  thinking  and  activity,  but 
to  describe  the  birth,  the  struggles,  and  the  end  of  the  uni- 
verse. 


POLARIZATION 


E              C 

C'            L 

FIG.  17 


LET  me  direct  your  attention  to  an  experiment  that  you 
may  all  repeat  without  difficulty.  I  take  a  sheet  of  ordi- 
nary glass,  ACB  (Fig.  17),  and  hold  it  between  my  eye,  E, 
and  the  light,  L,  so  that  EL  is  perpendicular  to  the  plane  of 
the  glass.  As  I  turn  the  glass  round,  keeping  0  unmoved, 
and  the  plane  of  the  glass 
always  at  right  angles  to 
EL,  the  light  maintains  a 
uniform  brightness.  Now 
I  put  in  a  second  sheet  of 
glass,  A'C'B',  and  hold  it 
parallel  to  the  first.  The 
light  does  not  look  quite  as 
bright  as  before,  but  it  is  still  true  that  its  intensity  is  un- 
changed by  any  turning  of  the  first  piece  of  glass  in  the 
manner  that  has  been  described.  Next  let  us  modify  this 
experiment  by  substituting  for  the  glass  a  substance  almost 
as  transparent.  Here  is  some  Iceland  spar  made  into  the 
form  of  a  Nicol's  prism.  On  putting  it  before  the  light  of 
the  lantern,  you  see  how  transparent  it  is  by  observing  how 
brilliantly  the  screen  is  illuminated  by  the  light  that 
streams  through  the  prism.  Another  prism  similar  to  the 
first  is  now  introduced,  and  you  observe  that  as  this  prism 
is  turned  round,  exactly  as  was  the  glass  with  which  we 
began,  the  brightness  of  the  screen  is  no  longer  constant, 

95 


96  LIGHT 

but  is  varying  continuously.  Now  the  screen  is  exceed- 
ingly bright,  and  now  that  I  have  turned  the  prism  a  greater 
way  round  through  ninety  degrees,  there  is  no  light  at  all 
on  the  screen.  Further  turning  gradually  restores  the  light 
until  a  full  half  turn  has  been  made,  when  the  screen  is  as 
brightly  lit  up  as  ever,  and  so  the  cycle  goes  on  until  again 
all  the  light  is  extinguished.  This  is  certainly  a  curious 
phenomenon,  the  cutting  off  of  light  by  means  of  a  trans- 
parent substance  merely  by  holding  it  in  the  right  position. 
The  explanation  of  the  phenomenon  involves  the  discus- 
sion of  the  polarization  of  light,  a  subject  interesting  in 
itself  and  of  the  first  importance  in  the  development  of 
optical  theory. 

You  have  already  been  reminded  that  light  is  to  be  re- 
garded as  due  to  a  to-and-fro  oscillation,  a  wave-motion 
propagated  in  a  medium  that  is  called  the  ether.  Let  us 
suppose  that  such  a  disturbance  enters  this  room  by  the 
north  wall  and  that,  at  any  instant  of  time,  every  element 
of  ether  on  that  wall  is  moving  similarly.  We  should  speak 
of  this  wall  as  the  wave-front,  and  in  due  time,  as  the  dis- 
turbance was  passed  on  from  element  to  element,  this  wave- 
front  would  move  across  the  room  and  reach  the  south  wall. 
So  far  we  have  said  nothing  as  to  the  direction  of  motion  of 
each  element  in  the  wave-front;  we  have  merely  said  that 
the  motion  is  of  a  vibratory  character,  each  point  moving 
to  and  fro  and  returning  to  its  original  position  with  a 
definite  frequency.  It  now  becomes  necessary  to  specify 
more  definitely  the  character  of  this  motion,  and  the  first 
point  to  bear  in  mind  is  that,  for  reasons  that  will  be  in- 
dicated almost  immediately,  we  must  think  of  all  the  ele- 
ments in  a  wave-front  as  moving  entirely  in  that  plane. 
In  the  case  just  referred  to,  if  we  could  see  the  ethereal 


POLARIZATION  97 

elements  as  the  light  entered  the  north  wall  of  the  room, 
each  of  these  elements  would  be  moving  in  a  little  orbit, 
every  point  of  which  would  be 
on  the  north  wall.  Of  course 
this  restricts  the  possible 
movements  of  the  ether  very 
much;  it  confines  them  all 
to  the  wave-front,  but  there 

is  still  a  great  deal  of  freedom.  Orbits  of  all  sorts  might 
be  described,  some  elements  might  be  vibrating  to  and  fro 
along  a  line,  some  in  circles,  others  in  ellipses,  and  others 
in  more  complex  orbits  —  always  with  the  restriction  that 

the  plane  of  these  orbits 
must   be   the   wave-front. 


ooo 

00 


OOO    Such  a  sYstem  of  multiform 
(*\      orbits  is  depicted  in  Fig. 


18,  the  plane  of  the  paper 
representing  the  wave- 
FlG-  19  front,  and  if  such  a  condi- 

tion of  things  existed,  the  light  would  not  be  polarized.  The 
peculiarity  of  polarized  light  is  that  all  these  orbits  are 
similar.  If  they  are  all  circles,  as  in  Fig.  19,  the  light  is 
said  to  be  circularly  polarized.  The  circular  orbits  may 
be  described  in  two  different 
senses,  clockwise  and  coun-  /^  f\  f\ 
ter-clockwise,  and  these  are  \_/  \J  \J 
usually  distinguished  as  right-  S\  S~\  s\ 

handed  and  left-handed  polar-  T  J        f  J        f  J 

ization.    Again,  the  orbits  may  FIQ  20 

be    all  similar   and    similarly 

situated  ellipses,  as  in  Fig.  20,  and  this  constitutes  elliptical 
polarization.    Or  all  the  elements  of  the  ether  may  vi- 


98  LIGHT 

brate  backward  and  forward  along  a  series  of  parallel  lines. 
This  is  rectilinear  polarization,  or  what  is  more  generally 
called  plane  polarization.  The  plane  at  right  angles  to 
the  wave-front  and  through  the  direction  of  displacement 
is  called  the  plane  of  polarization.  Fig.  21  represents  two 

cases    of    plane    polarized 
light,  the  planes  of  polari- 
, ,     » zation  being  at  right  angles 
/       T   >          to  one  another. 

The  case  last  dealt  with, 
that  of  plane  polarization, 

FIG.  21  .  /          .   i      .        ,.   .,  ; 

is  one  of  special  simplicity 

and  special  importance.  The  vibrating  elements  are  all 
moving  backward  and  forward  along  a  series  of  parallel 
lines.  This  type  of  motion  is  well  illustrated  by  look- 
ing at  a  string,  AB  (Fig.  22  a),  which  is  held  taut,  with 
its  ends  fixed  at  A  and  B.  If  the  string  be  plucked 
aside  very  slightly  at  C,  its  elements  will  vibrate  to 
and  fro  in  the  plane  ACB,  the  various  points  moving 
along  lines  at  right  angles  to  AB.  In  this  case  ACB 
is  the  plane  of  polarization,  and  it  should  be  noted  that, 
as  the  wave  of  disturbance  progresses  along  the  string,  the 
motion  of  each  point  is  in  the 

wave-front    at    right    angles   (a)  A L±i — ^~ -B 

to  the  string,  the  vibrations  r  „, 

f,\A _^      _^          C  V £ 

being  of  the  type  described  as    ^  '  ~*  FIG  2J* 

transverse  vibrations.    If  the 

vibrations  be  longitudinal  instead  of  transverse,  we  have  an- 
other important  type,  whose  leading  features  can  be  illus- 
trated by  the  motion  of  an  elastic  string,  AB,  which  is  kept 
taut  as  before.  If  now  a  point  C  be  moved  to  C"  (Fig. 
22  6)  along  the  string,  instead  of  at  right  angles  to  it, 


POLARIZATION  99 

a  longitudinal  wave  will  move  along  the  string,  and  the 
various  elements  will  vibrate  to  and  fro  in  the  direction 
AB.  These  two  types  of  vibrations  differ  in  one  very 
important  particular,  the '  transverse  can  be  polarized, 
the  longitudinal  cannot.  The  peculiarity  of  a  polarized 
vibration  is  that  each  of  the  moving  elements  is  con- 
strained to  move  in  a  similar  orbit,  and  it  is  evident 
that  this  can  be  done  with  the  string  vibrating  tranversely. 
With  the  longitudinal  vibrations,  on  the  other  hand,  only 
one  direction  of  motion  is  possible,  and  if  this  be  stopped, 
there  can  be  no  vibration  at  all.  Hence  it  follows  that 
if  light  can  be  polarized,  the  vibrations  must  be  of  the  trans- 
verse and  not  of  the  longitudinal  type ;  the  displacements  in 
the  ether  must  be  in  the  wave-front,  and  not  at  right  angles 
thereto.  We  shall  see  presently  that  the  experiment  made 
at  the  outset  of  this  lecture  with  the  Nicol  prisms  is  easily 
explained  if  we  recognize  the  possibility  of  polarization,  but 
otherwise  it  is  inexplicable.  It  is  for  this  reason  that  this 
experiment  is  crucial  in  the  theory  of  light.  The  idea  of 
accounting  for  optical  phenomena  by  ascribing  them  to 
motion  in  the  ether  is  an  old  one,  but  in  the  earlier  days 
this  ether  was  always  thought  of  as  an  extremely  rare 
medium,  a  sort  of  idealized  gas  rarer  than  anything  of 
the  kind  that  we  know  of  by  experience.  Now  a  gas  can 
not  propagate  vibrations  except  those  of  the  longitudinal 
type,  such  as  the  waves  in  the  air  that  produce  the  sensa- 
tion of  sound.  To  transmit  transverse  vibrations,  a  medium 
must  be  able  to  resist  certain  changes  of  shape;  it  must 
have  some  rigidity,  like  a  piece  of  steel.  This  proved  a 
great  stumbling-block  to  many,  even  to  such  leading  men 
of  science  as  Arago  and  Fresnel,  when  the  phenomena  of 
polarization  seemed  to  force  upon  them  the  idea  of 


100 


LIGHT 


transverse  vibrations  in  the  ether.  Fresnel  admitted  that 
he  "had  not  courage  to  publish  such  a  conception";  but 
Young  and  other  men  were  bolder,  so  that  the  idea  of 
transverse  ethereal  vibrations  is  now  a  commonplace, 
and  the  notion  of  an  ether  with  some  rigidity  has  lost  its 
terrors. 

We  have  already  made  use  of  a  vibrating  string  to  illus- 
trate the  meaning  of  a  plane  polarized  wave,  and  we  may 


FIG.  23 

use  it  also  to  throw  some  light  on  the  experiment  with  the 
Nicol  prisms  at  the  outset  of  this  lecture.  I  have  here  a  rope, 
and  as  I  move  one  end  of  it,  you  observe  a  wave  of  disturb- 
ance passing  along  the  rope,  and  the  rope  being  quite  free, 
the  displacements  may  be  in  any  directions  at  right  angles 
to  "the  rope.  Next  I  pass  the  rope  through  this  simple 
wooden  structure  P  of  Fig.  23.  You  will  observe  that  it 
is  a  box  divided  up  into  narrow  compartments  by  a  series  of 
parallel  partitions  that  are  just  wide  enough  apart  to  allow 
the  rope  to  pass  freely  between  two  consecutive  partitions. 
The  effect  of  passing  the  rope  through  this  apparatus  is  to 
polarize  the  wave  of  displacement  that  passes  along  the  rope. 
If  the  partitions  are  vertical,  the  displacements  are  all  con- 


POLARIZATION 


101 


fined  to  a  vertical  plane,  so  that  we  have  a  plane  polarized 
wave,  the  plane  of  polarization  being  vertical.  Now  if  I  take 
a  second  box,  A,  similar  to  the  first,  P,  and  hold  it  with  its 
partitions  vertical  (i.e.  parallel  to  those  of  the  first  box),  you 
will  observe  that  when  the  rope  is  passed  through  A  as  well  as 
P,  the  disturbance  that  gets  through  P  is  freely  transmitted 
through  A  also.  Suppose,  however,  I  turn  A  somewhat, 
so  that  its  partitions 
are  no  longer  parallel  to 
those  of  P,  then  you  will 
observe  that  A  destroys 
some  of  the  motion  in 
the  rope  after  it  has  been 
transmitted  through  P, 


and  that  when  A  is 
turned  so  that  its  parti- 
tions are  horizontal,  and 
therefore  at  right  angles  to  those  of  P,  then,  however  vio- 
lently I  move  the  end  of  the  rope,  there  is  absolutely  no  dis- 
turbance that  gets  through  both  boxes.  Now  we  shall  see 
in  a  later  lecture,  when  dealing  with  crystals,  that  a  crystal 
acts  upon  a  beam  of  light  somewhat  in  the  same  way  that 
this  apparatus  acts  upon  our  rope.  It  will  not  permit 
vibrations  to  pass  through  it,  unless  they  are  confined  to 
one  or  other  of  two  planes  at  right  angles.  The  effect  is  the 
same  as  if  we  had  a  number  of  obstacles  symmetrically 
arranged,  as  are  the  shaded  portions  of  Fig.  24.  Any  one 
setting  out  from  0  could  not  proceed  along  a  straight  line 
(such  as  Oa)  for  any  distance  without  being  stopped  by  an 
obstacle,  unless  they  moved  along  one  or  other  of  the  two  lines 
Ox  and  Oy,  which  are  at  right  angles  to  one  another.  A  to- 
and-fro  motion  along  these  directions  might  be  maintained 


FIG.  24 


102  LIGHT 

indefinitely,  but  in  no  other  direction  would  it  be  possible. 
The  Nicol's  prism  used  in  our  experiment  is  a  simple  and 
ingenious  instrument  made  of  the  crystal  Iceland  spar, 
and  so  arranged  that  of  the  two  waves  that  might  be  prop- 
agated (each  plane  polarized  at  right  angles  to  the  other) 
one  is  got  rid  of  by  total  reflection.  Thus  a  Nicol's  prism 
acts  upon  light  in  such  a  way  that  the  only  light  that  can 
get  through  the  prism  is  plane  polarized  in  what  is  known 
as  the  principal  plane  of  the  prism.  If,  then,  we  hold  two 
Nicols  with  their  principal  planes  parallel,  this  corresponds 
exactly  to  the  case  of  the  two  boxes  with  their  partitions 
parallel,  and  the  light  that  comes  through  the  first  is  freely 
transmitted  by  the  second.  On  turning  the  second  Nicol,  a 
change  is  made,  and  if  it  be  turned  so  that  the  two  Nicols 
are  crossed,  that  is,  if  their  principal  planes  be  at  right 
angles,  we  have  a  state  of  affairs  similar  to  that  with  the 
boxes,  the  partitions  of  one  being  vertical  and  of  the  other 
horizontal.  Under  such  circumstances  we  have  seen  that 
no  disturbance  in  the  rope  can  be  propagated  through 
both  boxes,  and  no  light  gets  through  both  Nicols. 

I  hope  that  enough  has  been  said  to  make  clear  the  mean- 
ing of  polarization,  and  particularly  of  plane  polarized  light. 
Now  when  a  beam  of  plane  polarized  light  passes  through  a 
solid  like  glass  or  a  liquid  like  water,  its  plane  of  polariza- 
tion on  emergence  is  the  same  as  it  was  at  entrance.  This, 
however,  is  not  the  case  with  all  substances,  a  large  number 
being  so  constituted  that  the  emergent  light  is  polarized  in 
a  different  plane  from  the  incident.  Under  such  circum- 
stances the  plane  of  polarization  has  been  rotated  through 
a  certain  angle,  and  this  phenomenon  is  consequently 
spoken  of  as  the  rotation  of  the  plane  of  polarization  of 
light,  or  more  briefly  as  rotatory  polarization.  If  you  care 


POLARIZATION  103 

to  see  the  phenomenon,  it  is  very  easily  exhibited  with 
the  apparatus  before  you.  You  will  observe  that  after 
a  little  adjustment  these  two  Nicols  are  now  "crossed/' 
with  their  principal  planes  at  right  angles,  so  that  no  light 
can  get  through  them  both.  Now  I  place  between  the 
Nicols  this  plate  of  quartz,  and  you  see  at  once  that  the 
screen  is  illuminated.  However,  on  turning  one  of  the 
Nicols  gradually,  you  see  that  we  reach  a  position  where 
darkness  once  more  reigns,  and  a  very  little  consideration 
will  show  you  that  this  is  what  we  should  expect  if  the 
quartz  has  the  power  of  rotating  the  plane  of  polarization 
of  the  light  that  passes  through  it,  and  that  the  amount  of 
this  rotation  is  measured  exactly  by  the  angle  through  which 
it  was  necessary  to  turn  the  Nicol  to  produce  darkness 
again  after  the  quartz  had  been  introduced.  This  phenome- 
non of  rotatory  polarization  is  a  very  interesting  one ;  we 
shall  be  occupied  with  it  exclusively  during  the  remainder 
of  this  lecture.  It  will  be  advisable,  however,  to  postpone 
the  consideration  of  the  very  important  case  when  the  rota- 
tion is  effected  by  the  influence  of  magnetism,  as  that  case 
will  be  taken  up  more  appropriately  when  we  are  dealing 
with  the  relations  between  light,  electricity,  and  magnetism 
in  the  concluding  lecture  of  this  course. 

Substances  that  are  endowed  with  the  power  of  rotating 
the  plane  of  polarization  of  light  may  differ  as  to  the  direc- 
tion as  well  as  the  magnitude  of  the  rotation  that  they 
produce  in  any  given  circumstances.  Some  may  rotate  the 
plane  as  if  you  were  turning  an  ordinary  screw  to  the  right, 
while  others  rotate  it  to  the  left.  Such  substances  are  dis- 
tinguished by  various  names,  such  as  right-handed  and  left- 
handed,  or  dextro-rotatory  and  laevo-rotatory,  and  wher- 
ever they  have  the  rotatory  power  at  all,  they  are  spoken 


104  LIGHT 

of  as  optically  active.  There  are  two  main  classes  to  be 
considered :  in  the  first  class  are  certain  crystals,  and  in  the 
second  certain  organic  substances  in  solution.  In  both  cases 
experiment  proves  that  the  angle  of  rotation  is  proportional 
to  the  thickness  of  the  active  medium  traversed  by  the 
light,  so  that  the  rotation  produced  by  a  given  thickness 
may  be  taken  as  a  measure  of  the  rotatory  power  of  the 
substance. 

The  most  obvious  thing  about  a  crystal  is  that  it  differs 
from  a  non-crystal  in  having  a  definite  structure.  It  is 
not  a  formless  thing  like  a  piece  of  glass.  If  you  could 
watch  the  process  of  crystallization,  you  would  see  a  definite 
form  being  built  up  as  if  by  the  unerring  hand  of  a  skilful 
artist.  You  might  expect,  then,  that  this  fundamental 
difference  between  crystalline  and  non-crystalline  media 
would  have  something  to  do  with  the  explanation  of  rota- 
tory power.  And  there  can  be  no  doubt  that  it  has,  the 
only  doubt  being  as  to  the  actual  arrangement  of  the  mole- 
cules in  any  crystal,  and  the  mode  in  which  this  arrangement 
makes  the  crystal  optically  active.  That  there  is  an  inti- 
mate relation  between  structure  and  rotatory  power  was 
shown  long  ago  by  Sir  John  Herschel.  It  was  known  that 
some  specimens  of  quartz  rotate  the  plane  of  polarization 
to  the  right,  while  others  rotate  it  to  the  left.  Herschel 
found  that  this  difference  went  hand  in  hand  with  certain 
differences  of  crystalline  form.  In  the  quartz  of  one  class 
certain  facets  of  the  crystal  were  found  on  minute  examina- 
tion to  lean  all  in  one  direction,  —  to  the  right,  say,  — 
whilst  with  the  other  class  the  corresponding  facets  leaned 
to  the  left.  The  first  class  was  dextro-rotatory,  the  sec- 
ond IsBVO-rotatory.  And  had  there  been  any  doubts  that 
rotatory  power  is  due  to  structure,  these  must  have  been 


POLARIZATION 


105 


removed  by  the  consideration  of  the  fact  that  the  optical 
activity  of  a  substance  disappears  when  its  crystalline 
structure  is  destroyed,  as  happens  to  quartz  when  it  is 
fused,  or  to  camphor  when  it  is  dissolved. 

Crystalline  structure  may  produce  rotation,   but  how 
does  it  effect  it?    This  is  a  question  not  easy  to  answer 


Q' 


FIG.  25 


satisfactorily,  especially  within  the  limits  of  such  a  lecture 
as  this,  but  perhaps  I  may  give  you  some  glimpses  of  what 
has  been  done  to  solve  the  mystery.  It  is  first  necessary 
to  realize  that  what  looks  like  a  plane  polarized  beam  of 
light  may  really  be  a  combination  of  two  equal  and  opposite 
circularly  polarized  beams,  the  orbits  of  the  two  circles 
being  described  in  opposite  senses.  Suppose  that  we  set 
two  particles  off  from  C  (Fig.  25  a)  with  equal  speeds  in 
opposite  senses  in  the  circle,  one  going  round  clockwise 
and  the  other  counter-clockwise.  After  a  time  they  will 
arrive  at  the  points  B  and  A  respectively,  where  B  is  just 
as  far  above  the  level  COC'  as  A  is  below  it.  Now  if  we 
raise  a  point  a  distance  BN  by  means  of  one  motion,  and 
lower  it  an  equal  distance,  AN,  by  means  of  the  other  t  the 
effect  of  the  combined  motions  is  to  keep  the  particle  at 
the  level  N  on  the  line  COG'.  Thus  the  combined  effect  of 
two  equal  and  opposite  circular  motions  is  exactly  equiva- 


106  LIGHT 

lent  to  a  vibration  along  the  straight  line  COCf ;  in  other 
words,  what  looks  like  rectilinear  (or  plane)  polarization 
may  really  consist  of  a  combination  of  two  opposite  circular 
polarizations.  Let  us  suppose,  in  the  next  place,  that  the 
two  particles  do  not  set  out  simultaneously  from  (7,  but 
that  one  starts  from  C  and  moves  round  the  circle  in  a 
clockwise  sense,  while  the  other  goes  in  the  opposite  sense, 
and  starts  from  E  (Fig.  25  6).  It  will  be  seen,  as  before, 
that  the  combination  of  these  two  motions  is  equivalent 
to  a  vibration  along  the  straight  line  QOQ',  which  is  such 
that  OQ  bisects  the  angle  EOC.  Think  next  of  a  right- 
and  a  left-handed  circularly  polarized  wave  moving  through 
a  crystal,  and  that,  owing  to  the  peculiar  structure  of  the 
crystal,  these  two  waves  move  through  the  crystal  with 
different  speeds.  The  two  waves  will  take  a  different 
time  to  traverse  a  given  thickness  of  the  material,  so  that 
one  will  get  through  the  plate  faster  than  the  other.  A 
point  in  the  left-handed  wave  (let  us  say)  will,  while  the  wave 
has  traversed  the  plate,  have  made  a  certain  number  of 
complete  revolutions  and  come  back  to  its  starting-point 
C  (Fig.  25  b) ;  the  corresponding  point  in  the  other  wave 
will  have  had  more  time  when  that  wave  emerges  from  the 
plate,  and  will  have  arrived  at  E.  Once  through  the  plate 
and  into  the  surrounding  non-crystalline  medium,  the  two 
waves  will  proceed  at  equal  speeds,  so  that  their  combined 
effect  will  correspond  to  that  of  two  circular  motions  de- 
scribed in  opposite  senses  at  the  same  rate,  one  starting  from 
C  and  the  other  from  E.  We  have  already  seen  that  these 
two  are  equivalent  to  a  vibration  along  a  straight  line  Q'OQ, 
or  to  plane  polarized  light.  However,  the  plane  of  polariza- 
tion will  now  be  Q'OQ,  whereas  it  was  C'OC  on  entering 
the  crystalline  plate ;  in  other  words,  the  crystal  will  have 


POLARIZATION  107 

rotated  the  plane  of  polarization  through  an  angle  repre- 
sented by  COQ. 

It  remains  only  to  consider  what  structure  would  give 
rise  to  different  speeds  for  right-  and  left-handed  waves. 
An  almost  endless  variety  of  such  structures  might  be 
suggested ;  almost  anything  would  serve  the  purpose  that 
would  present  a  lack  of  symmetry  to  a  clockwise  and  a 
counter-clockwise  circu- 
lar motion.  Suppose 
that  we  could  watch  a 
crystal  being  built  up, 
as  it  is  when  the  solid 
slowly  crystallizes  out  of 
the  mother  liquor.  Each 
molecule,  or  group  of 
molecules,  when  it  fell  -, 

llG. 

down,  would  take  up  its 

place  on  the  solid  already  formed,  and  it  would  do  this  not 
in  a  random  fashion,  but  according  to  some  definite  rule,  as 
if  in  obedience  to  some  inexorable  law  of  its  being.  Thus 
each  group  might  be  shaped  somewhat  as  shown  in  Fig.  26, 
and  the  different  groups  piled  on  one  another  in  the  fashion 
there  depicted.  Under  such  circumstances  the  crystal  would 
present  a  lack  of  symmetry  as  regards  right-  and  left-handed 
rotation.  It  is  easy  to  imagine  a  great  variety  of  patterns 
that  would  be  similarly  unsymmetrical,  and  much  ingenuity 
has  been  displayed  in  building  up  artificial  media  in  some 
such  way  as  this,  and  arranging  them  so  as  to  endow  the 
structure  with  optical  rotatory  power.  Thus  Reusch 
showed  that  by  superposing  thin  films  of  mica  according 
to  a  simple  law,  the  rotatory  power  of  quartz  could  be 
reproduced  in  all  its  details.  More  recently,  under  the 


108 


LIGHT 


guidance  of  the  electric  theory  of  matter,  it  has  become 
common  to  estimate  the  influence,  in  rotating  the  plane 
of  polarization,  of  groups  of  electrons  arranged  in  an  un- 
symmetrical  manner.  With  certain  simple  assumptions 
it  is  possible  to  express  the  ideas  in  the  exact  language  of 
mathematics,  and  so  to  test  the  theory  in  a  quantitative  way 
by  seeing  to  what  extent  it  agrees  with  the  most  careful 
measurements  of  rotation.  There  are  two  such  tests  of 
any  theory :  first,  it  must  indicate  the  relation  between  the 
amount  of  rotation  and  the  thickness  of  the  medium  that 
is  traversed;  and  second,  it  must  show  in  what  way  the 
rotation  depends  upon  the  color  (or,  in  other  words,  the 
frequency)  of  the  light.  Any  theory  such  as  has  been 
suggested  above  shows  that  whatever  be  the  color  of  the 
incident  light,  the  amount  of  rotation  should  be  propor- 
tional to  the  thickness  of  the  active  substance  through 
which  the  light  passes,  i.e.  it  should  be  twice  as  great  for 
two  inches  as  for  one.  The  following  table  gives  the  rota- 
tion produced  by  two  plates  of  quartz,  one  being  1  milli- 
meter, and  two  others  7^  millimeters  in  thickness,  the  rota- 
tions being  given  in  degrees  for  various  colored  lights :  — 


THICKNESS 

BED 

CHANGE 

YELLOW 

GREEN 

BLUE 

INDIGO 

VIOLET 

1  mm.     .     .     . 

18 

gj| 

24 

29 

31 

36 

42 

7.5  mm.  .     .     . 

135 

161J 

180 

217£ 

232£ 

270 

315 

It  will  be  observed  that  the  amount  of  rotation  with 
each  color  follows  the  law  of  proportionality  to  the  thick- 
ness, just  as  the  theory  indicates.  The  theory  also  shows 
that  the  relation  between  the  amount  of  rotation  and  the 
frequency  of  the  vibrations  in  the  light  is,  for  a  substance 


POLARIZATION 


109 


like  quartz,  given  by  a  formula  of  the  type  R  =  a/2+ 


J 


J  ~~ 


when  R  is  the  rotation,  /  the  frequency,  and  a,  b, 
and  /!  are  constants  depending  on  the  nature  of  the  sub- 
stance. How  closely  this  fits  the  facts  is  shown  in  the 
following  table,  which  compares  the  theoretical  and  the 
observed  natures  of  R  for  the  case  of  quartz,  R  denoting 
the  rotation  in  degrees  produced  by  a  plate  one  millimeter 
in  thickness,  and  /  being  the  frequency  in  million  millions 
per  second  :  — 


f 

140.12 
1.57 
1.60 

169.41 
2.29 
2.28 

206.80 
3.43 
3.43 

277.65 
6.23 
6.18 

447.01 
16.56 
16.54 

456.89 
17.33 
17.31 

508.82 
21.70 
21.72 

517.85 
22.53 
22.55 

519.74 
22.70 

22.72 

R  (theory)  .  . 
R  (observation) 

f 

549.09 
25.51 
25.53 

589.57 
29.67 
29.72 

609.92 
31.92 
31.97 

624.70 
33.60 
33.67 

687.97 
41.46 
41.55 

740.98 
48.85 
48.93 

871.53 
70.61 
70.59 

1091.7 
121.34 
121.06 

1367.1 
220.57 
220.72 

R  (theory)  .  . 
R  (observation) 

So  far  we  have  been  dealing  with  substances  that  lose 
their  rotatory  power  when  they  are  brought  into  a  liquid 
state  by  fusion  or  solution.  There  exists,  however,  a  large 
number  of  substances  that  have  this  power  although  they 
are  liquids,  and  that  retain  it  even  when  the  liquid  is 
turned  into  a  vapor.  Thus,  in  1815,  Biot  discovered  that 
turpentine  is  optically  active,  this  important  discovery,  like 
several  others  in  science,  being  accidental,  as  it  was  made 
when  Biot  was  searching  for  something  quite  different. 
Two  years  later  the  same  physicist  made  a  discovery  that 
is  still  more  interesting  from  our  point  of  view.  He  looked 
for  rotatory  power  in  the  vapor  of  turpentine,  and  actually 
observed  it.  His  most  conclusive  results  were  obtained 
when  working  with  vapor  in  a  tube  about  fifty  feet  long,  set 


110  LIGHT 

up  in  an  old  church  at  Luxembourg.  However,  although 
he  saw  clearly  that  there  was  rotation  of  the  plane  of 
polarization  of  the  light  that  had  passed  through  this  tube, 
he  was  prevented  from  measuring  it  accurately,  as  the 
inflammable  vapor  ignited  and  destroyed  his  apparatus. 
Science  had  to  wait  nearly  half  a  century  until  the  investi- 
gation was  resumed  in  1864  by  Gernez.  He  succeeded  in 
determining  the  rotations  produced  by  various  liquids  and 
in  showing  that  their  rotatory  power  is  retained  when  they 
are  transformed  into  the  state  of  vapor.  This  is  a  very 
striking  result,  in  view  of  what  has  been  said  as  to  the 
probable  explanation  of  optical  activity.  This  power  has 
been  ascribed  to  structural  arrangement,  and  yet  there 
seems  no  possibility  of  permanent  structure  with  the 
molecules  of  a  vapor  which  are  in  constant  motion.  This 
seems  to  drive  us  to  the  hypothesis  of  structure  not  of  the 
molecules,  but  in  the  molecules  themselves.  The  atoms  of 
which  the  molecules  are  built  may  be  arranged  in  such  a  way 
as  to  produce  optical  activity,  so  that  the  study  of  our 
subject  lures  us  into  the  rich  and  expansive  field  of  Stereo- 
chemistry. This  is  that  fruitful  department  of  modern 
chemistry  that  concerns  itself  with  the  arrangement  of 
atoms  in  space  and  seeks  to  determine  how,  if  you  were 
making  a  model  of  a  molecule,  you  would  place  the  different 
atoms  of  which  it  is  composed.  We  have  time  only  for  a 
hurried  glance  into  this  field,  enough  perhaps  to  stimulate 
our  desire  for  further  knowledge  and  to  break  down  a  por- 
tion of  the  arbitrary  boundary  that  has  been  set  up  between 
chemistry  and  physics. 

The  first  epoch-making  work  in  the  direction  that  has 
just  been  indicated  was  that  of  Pasteur,  who,  in  1848,  took 
up  the  study  of  the  rotatory  power  of  different  forms  of 


POLARIZATION  111 

tartaric  acid.  He  found  it  possible  to  separate  this  acid 
into  four  different  classes,  all  with  the  same  chemical 
constitution  (i.e.  made  up  of  the  same  elements),  but  with 
different  physical  structure  and  different  optical  power. 
Two  of  the  classes  were  optically  inactive,  and  two  had 
rotatory  power.  One  of  the  inactive  acids  had  the  pecul- 
iarity that  when  it  was  crystallized,  its  crystals,  on  careful 
examination,  proved  to  be  separable  into  two  distinct  types, 
whereas,  with  the  other  inactive  acid,  the  crystals  were  not 
thus  separable.  The  two  types  of  crystals  that  have  just 
been  mentioned  as  constituting  together  the  inactive  acid 
of  the  first  class,  differed  from  one  another  in  a  simple  yet 
remarkable  manner.  Their  points  of  resemblance  and  of 
contrast  were  exactly  like  those  of  certain  objects  and  their 
images  as  seen  in  a  plane  mirror.  Your  right  and  left  hand 
have  many  points  of  likeness,  but  yet  they  are  quite  differ- 
ent. They  are  not  superposable ;  twist  the  right  hand 
as  you  will,  and  it  refuses  to  fit  into  a  glove  made  for  the 
left.  If  you  hold  the  right  hand  before  a  mirror,  and  look 
at  the  image,  you  will  see  a  left  hand,  so  that  the  relation 
between  the  two  types  of  crystals  under  discussion  might 
be  indicated  by  saying  that  one  type  was  left-handed  and 
the  other  right-handed.  Pasteur,  after  separating  these 
types  from  one  another,  formed  a  solution  of  each.  The 
right-handed  type  was  found  to  have  the  same  chemical 
constitution  as  the  original  acid  of  which  it  formed  a  part ; 
but  instead  of  being  inactive,  it  had  rotatory  power.  It  rotated 
the  plane  of  polarization,  let  us  say,  to  the  right,  and  so 
was  ctoro-rotatory.  The  left-handed  type  had  also  the 
same  chemical  constitution,  but  it,  too,  was  optically  active 
and  too-rotatory.  The  presence  of  equal  quantities  of 
these  two  types  in  the  original  acid  explained  its  inactivity, 


112  LIGHT 

for  each  neutralized  the  other,  the  right-handed  rotation 
produced  by  the  first  type  being  exactly  counterbalanced 
by  the  left-handed  rotation  of  the  second.  From  the  con- 
sideration of  these  and  similar  phenomena,  Pasteur  was 
led  to  make  the  general  statement  that  all  organic  com- 
pounds could  be  divided  into  one  or  other  of  two  groups, 
according  to  the  form  of  their  molecular  arrangement.  It 
will  be  observed  that  not  every  object  differs  in  appearance 
from  its  image  in  a  plane  mirror ;  in  the  case  of  a  perfectly 
regular  figure,  such  as  a  cube  or  a  regular  tetrahedron, 
object  and  image  are  superposable.  On  the  other  hand, 
with  such  objects  as  a  screw,  an  irregular  tetrahedron,  or 
the  hand,  object  and  image  are  not  superposable.  Pasteur 
suggested  that  when  the  arrangement  of  the  atoms  fell 
into  the  first  of  these  classes  there  would  be  molecular  sym- 
metry, and  the  substance  would  be  optically  inactive ;  but 
a  group  belonging  to  the  second  class  would  represent  mo- 
lecular asymmetry,  and  rotatory  power  would  be  expected. 
After  Pasteur's  researches,  the  next  great  impetus  to 
work  in  this  field  was  given  in  1874  by  the  speculations 
of  Van't  Hoff  and  Le  Bel.  The  fundamental  conception 
here  was  a  definite  arrangement  of  atoms,  the  so-called 
tetrahedral  molecule,  which  has  formed  the  basis  of  the 
larger  part  of  later  speculations  in  stereochemistry.  It  is 
now  a  commonplace  of  the  text-books,  and  it  would  be 
out  of  place  to  discuss  it  here  further  than  is  necessary  to 
give  a  general  impression  of  the  main  ideas,  in  so  far  as 
they  throw  any  light  on  the  problem  of  optical  activity. 
We  have  already  remarked  that  the  fundamental  idea  of 
stereochemistry  is  that,  in  a  given  compound,  the  atoms 
composing  a  molecule  are  arranged  in  a  definite  form,  and 
the  fundamental  problem  is  to  determine  that  form  for 


POLARIZATION  113 

different  compounds.  Now  Van't  Hoff's  hypothesis  is 
that,  in  the  case  of  organic  compounds,  the  arrangement 
is  such  that  the  different  atoms,  or  groups  of  atoms,  occupy 
the  four  corners  ABCD  (Fig.  27)  of  a  tetrahedron,  the 
carbon  element  being  in  the  center.  If  this  were  so,  it 
would  be  convenient  to  separate  carbon  compounds  into  two 
classes,  in  the  first  of  which  there  is  only  one  carbon  atom 
present,  and  in  the  second  there  are 
two  or  more  such  atoms.  In  the 
first  class,  if  the  four  groups  at  the 
corners  of  the  tetrahedron  were  all 
different,  any  arrangement  and  its 
optical  image  would  be  different. 
Thus  every  form  would  have  its  as- 
sociate, and  as  each  would  be  unsym- 
metrical,  they  would  both  be  optically 
active,  one  rotating  to  the  right  and  the  other  to  the  left. 
A  compound  made  up  of  equal  parts  of  these  two  forms 
would  be  neutral,  and  so  optically  inactive.  Hence  in  this 
class  we  should  expect  three  modifications  of  any  arrange- 
ment :  one  dextro-rotatory,  another  Isevo-rotatory,  the 
third  inactive.  In  the  second  class,  where  there  were 
more  than  one  asymmetric  carbon  atom  in  the  molecule, 
the  number  of  possibilities  would  be  greater.  The  case  of 
tartaric  acid  has  already  been  described.  Here  we  have 
four  different  forms  —  one  dextro-rotatory,  another  laevo- 
rotatory,  a  third  inactive,  being  compounded  of  equal  pro- 
portions of  the  first  two,  and  a  fourth  also  inactive,  but 
for  a  different  reason.  This  inactive  form  differs  from  the 
other  in  that  it  cannot  be  resolved  into  active  constituents. 
The  molecule  is  built  up  of  two  similar  halves,  so  that 
there  is  optical  compensation  within  the  molecule  itself. 


114  LIGHT 

A  great  deal  of  work  has  been  done  in  this  field  since  1874, 
and  there  has  been  much  to  give  support  to  the  main  lines  of 
the  theory  here  set  forth.  It  has  been  found  that  there  is 
no  rotatory  power  in  any  compound  that  does  not  contain 
an  asymmetric  carbon  atom,  and  that  by  introducing  or  re- 
moving such  atoms  from  a  substance  the  power  of  optical 
activity  can  be  made  to  come  or  go.  Many  of  the  difficul- 
ties that  early  presented  themselves  have  been  removed. 
Thus,  at  the  outset,  several  substances  that  contain  an  asym- 
metric carbon  atom  were  found  to  be  inactive,  contrary  to 
the  theory;  but  later  research  has  shown  either  that  such 
substances  really  possess  some  rotatory  power  (although  a 
feeble  one),  or  that  they  consist  of  mixtures  in  equal  quan- 
tities of  two  oppositely  rotating  constituents,  or  that  they 
are  made  up  of  two  similarly  constituted  halves,  which, 
although  not  separable,  have  oppositely  rotating  powers. 
Of  special  importance  in  this  domain  have  been  the  re- 
searches of  E.  Fischer  on  the  members  of  the  sugar  group. 
If  Van't  Hoff's  hypothesis  be  right,  then  it  is  a  simple  prob- 
lem of  permutations  and  combinations  to  predict  the  num- 
ber of  different  modifications  that  should  be  possible  with 
a  given  group  of  atoms.  If  the  mathematical  problem  be 
too  hard  or  too  repellent,  you  may  reach  the  answer  by  the 
aid  of  models  and  a  little  patient  trial.  You  have  merely 
to  attach  a  series  of  differently  colored  balls  to  the  corners 
of  a  tetrahedron,  and  see  how  many  different  arrangements 
it  is  possible  to  make.  In  doing  this  you  may  learn  more 
than  the  mere  number  of  different  forms  in  which  the  com- 
pound could  exist,  for,  by  observing  the  salient  points  of 
resemblance  and  contrast  between  different  arrangements, 
you  may  get  hints  as  to  the  significance  of  these  for  chem- 
istry and  for  optics.  Thus,  when  Fischer  was  working  on 


POLARIZATION  115 

the  members  of  the  sugar  group,  he  made  a  careful  examina- 
tion of  dextrose,  and  concluded  from  its  chemical  reactions 
that  the  atoms  in  the  molecule  were  arranged  in  a  certain 
way.  The  arrangement  was  not  symmetrical,  and  the 
substance  was  optically  active  of  the  right-handed  rotatory 
type.  Fischer  concluded  that  there  might  be  expected  to 
exist  another  form,  the  arrangement  of  whose  atoms  would 
be  related  to  that  just  mentioned  in  the  same  way  as  an 
object  and  its  image  in  a  mirror.  He  succeeded,  after  care- 
ful trial,  in  actually  isolating  such  a  form,  one  that  was 
also  optically  active,  but  of  the  left-handed  rotatory  type. 

Perhaps  enough  has  been  said  to  indicate  that  the  hy- 
pothesis of  a  definite  arrangement  of  the  atoms  in  the  mole- 
cules of  a  substance  is  not  a  mere  idle  speculation.  It  has 
proved  a  very  useful  conception  in  modern  chemistry,  but 
our  interest  in  it  here  is  mainly  for  the  light  it  throws  on  the 
problem  of  optical  activity.  We  have  seen  that  rotatory 
power  is  always  associated  with  an  asymmetrical  arrange- 
ment of  the  atoms,  and  when  dealing  earlier  with  quartz 
and  similar  active  solids,  we  remarked  that  lack  of  sym- 
metry would  result  in  right-  and  left-handed  circularly 
polarized  waves  traversing  the  medium  with  different 
speeds,  and  so  would  account  for  the  rotation  of  the 
plane  of  polarization.  . 

Apart,  however,  from  all  such  speculations,  it  may  be 
well  to  remark  that  there  is  no  doubt  about  the  fact  of 
rotation,  so  that,  whether  these  theories  find  favor  or  not, 
we  may  make  use  of  this  fact  in  any  way  that  seems  good 
to  us.  The  facts  that  are  simplest  and  most  important 
to  bear  in  mind  are  as  follows:  Not  every  substance  is 
optically  active,  but  many  possess  this  power  of  rotating 
the  plane  of  polarization  of  a  beam  of  light  that  passes 


116  LIGHT 

through  them.  The  amount  of  the  rotation  is  found  to 
depend  on  the  temperature,  and  also  on  the  color  of  the 
light  that  is  employed.  For  light  of  a  definite  color  (e.g. 
that  of  one  of  the  sodium  lines),  the  rotation  varies  directly 
as  the  thickness  of  the  substance  traversed  by  the  light. 
In  the  case  of  liquids  it  depends  also  very  markedly  on  the 
strength  of  the  solution,  and  this  has  given  rise  to  a  very 
simple  and  very  important  plan  for  estimating  the  strength 
of  a  given  solution.  It  could  be  carried  out  with  the  ap- 
paratus used  in  the  experiment  with  which  this  lecture  was 
begun.  Let  light  from  a  sodium  flame  pass  through  the 
first  of  these  Nicol's  prisms.  It  issues,  as  we  have  seen,  as 
plane  polarized  light,  and  we  can  determine  the  plane  of 
polarization  exactly  by  noting  the  position  in  which  the 
second  Nicol  must  be  placed  in  order  to  cut  off  all  the  light 
from  the  screen.  Now  put  a  vessel  containing  an  optically 
active  solution  between  the  Nicols,  and  you  will  find  that 
the  second  Nicol  must  be  turned  through  a  certain  angle 
in  order  once  more  to  completely  cut  off  the  light  from  the 
screen.  If  you  have  a  means  of  measuring  carefully  the 
angle  through  which  the  Nicol  was  turned,  you  know  ex- 
actly the  rotation  of  the  plane  of  polarization  that  this 
solution  has  produced.  If,  then,  by  previous  experiment, 
you  have  determined  the  strength  of  solution  that  produces 
that  amount  of  rotation,  you  realize  that  your  problem  is 
solved.  I  have  suggested  the  use  of  Nicols,  but  of  course 
other  means  of  producing  polarization  may  be  employed.  A 
great  variety  of  polarizing  apparatus  has  been  invented  and 
is  constantly  being  used  to  determine  the  strengths  of  solu- 
tions of  such  substances  as  nicotine,  cocaine,  starch,  and 
alcohol,  and  most  important  of  all,  considering  the  magni- 
tude of  the  commercial  interests  involved,  of  sugar. 


POLARIZATION  117 

It  may  seem  a  curious  ending  to  a  lecture  that  deals 
entirely  with  what  seems  almost  painfully  "  unpractical/' 
—  polarization,  rotatory  power,  molecular  structure,  and 
the  like,  —  to  refer  to  means  of  measuring  the  strength  of 
alcohol  or  the  value  of  a  cargo  of  sugar.  If,  however,  you 
know  anything  of  the  history  of  science,  you  will  not  think 
it  strange  at  all,  but  will  rather  be  inclined  to  regard  it  as 
typical  of  almost  countless  similar  cases.  No  wise  man 
would  undertake  to  draw  quite  clearly  the  line  between 
" practical"  and  "unpractical,"  between  "useful"  and 
"useless,"  knowledge.  By  all  means  let  us  be  practical 
and  useful,  but  let  us  use  these  terms  in  no  narrow  sense, 
nor  suppose  for  a  moment  that  the  race  will  advance  most 
rapidly,  even  with  material  things,  by  sticking  closely 
to  what  is  obviously  "practical."  If  our  ancestors  had 
always  been  sticklers  for  "practical"  knowledge,  we  should 
probably  still  be  eating  acorns. 


VI 

THE    LAWS   OF    REFLECTION   AND   REFRACTION 

IN  the  opening  lecture  of  this  course  it  was  remarked 
that  man's  knowledge  of  optical  laws  might  be  summed 
up  almost  to  Newton's  day  within  the  compass  of  a  single 
sentence.  Of  general  principles  all  that  was  known  was 
the  fact  and  the  law  of  reflection  (as  regards  direction  only), 
the  fact  of  total  reflection,  and  the  fact  of  refraction.  It 
is  difficult  for  any  but  a  specialist  to  realize  what  enormous 
advances  have  been  made  since  then,  both  in  observation 
and  in  theory.  We  now  have  a  great  variety  of  instru- 
ments of  precision  that  enable  us  to  observe  most  optical 
phenomena  with  marvellous  accuracy,  and  a  theory  has 
been  developed  that  enables  us  to  group  together  the  whole 
mass  of  facts  with  the  utmost  simplicity  and  with  almost 
startling  success.  Few  men  are  in  a  position  to  understand 
the  searching  nature  of  the  test  that  can  now  be  applied 
to  optical  theories,  and  to  appreciate  how  well  the  modern 
theory  stands  the  test.  Not  until  you  have  put  yourself 
in  such  a  position  can  you  understand  the  confidence  of  a 
modern  physicist  in  his  theories.  He  is  no  longer  content 
with  a  mere  descriptive  theory  which  tells  him  in  a  general 
way  that  such  and  such  phenomena  are  to  be  expected. 
His  theory  must  enter  into  the  minutest  details  and  predict 
quantitatively.  It  must  tell  him  that  if  he  measures  this 
or  that  with  sufficient  accuracy,  he  will  find  its  measure  to 
be  so  and  so.  In  the  case  of  the  modern  theory  of  light, 

118 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        119 

all  the  improvements  and  all  the  refinements  of  modern 
instruments  but  tend  to  confirm  the  correctness  of  the  pre- 
diction. I  have  already  given  you  instances  of  this  (for 
example,  when  dealing  with  dispersion) ;  but,  even  at  the 
risk  of  wearying  you  with  figures  and  with  tables,  I  must 
give  you  more  of  a  similar  kind  to-night  and  in  later  lectures. 
Let  us  look  first  at  the  simpler  and  more  generally  known 
laws  of  reflection  and  refraction.  These  deal  only  with 
the  directions  of  the  various 
rays,  and  show  how  to  de- 
termine the  directions  of 
the  reflected  and  refracted 
ray  of  light  when  that  of 
the  incident  ray  is  given. 
In  Fig.  28  AB  represents 
an  incident  ray  which 
strikes  a  reflecting  surface 
BK  at  the  point  B,  in  such 
a  way  that  part  of  the  light  is  reflected  along  the  ray  BO, 
and  the  rest  refracted  along  BH.  If  EBF  be  drawn  at 
right  angles  to  the  reflecting  surface,  the  plane  containing 
AB  and  BE  is  called  the  plane  of  incidence.  The  law 
of  reflection,  which  determines  the  direction  of  the  re- 
flected ray,  states  that  BC  is  in  the  plane  of  incidence 
and  that  the  angle  EBO  is  exactly  equal  to  the  angle 
EBA,  orr  =  i,  with  the  notation  indicated  in  the  figure. 
The  law  of  refraction  (sometimes  called  Snell's  law, 
having  first  been  laid  down  by  Snell  in  1621)  states  that 
the  refracted  ray  BH  is  also  in  the  plane  of  incidence, 
and  that  the  angle  FBH  is  connected  with  the  angle 
A  BE  by  the  relation  sin  i  =  /A  sin  r',  where  /A  is  a  constant 
depending  on  the  nature  of  the  two  media  on  each  side  of 


120  LIGHT 

BK,  and  known  as  the  relative  refractive  index  of  these 
media.  (If  the  space  above  BK  is  a  vacuum,  then  n  is 
the  absolute  refractive  index,  or  simply  the  refractive  index 
of  the  medium  below  BK.)  As  it  is  impossible  to  find  an 
angle  whose  sine  is  greater  than  unity,  SnelFs  law  shows  that 
r'  could  not  be  found  if  the  angle  of  incidence  i  were  such 
that  sin  i  were  greater  than  n,  the  relative  refractive  index. 
If  the  first  medium  be  more  highly  refractive  than  the  sec- 
ond, for  example,  if  the  first  be  water  and  the  second  air,  then 
the  relative  refractive  index  //.  is  less  than  unity,  and  the 
angle  whose  sine  is  equal  to  fi  is  called  the  critical  angle. 
Under  such  circumstances  r'  would  be  impossible  if  the 
angle  of  incidence  i  were  greater  than  the  critical  angle  — 
so  that  we  should  expect  that  there  would  be  no  refracted 
ray,  and  that  all  the  light  would  be  reflected.  This  is  the 
phenomenon  of  total  reflection  that  was  brought  before  your 
notice  in  the  first  lecture,  and  the  point  to  be  noticed  now 
is  that  Snell's  law  indicates  exactly  the  conditions  under 
which  this  phenomenon  is  to  be  expected. 

All  these  laws  with  reference  to  reflection,  refraction, 
and  total  reflection  have  been  verified  experimentally  with 
the  greatest  precision.  Of  all  the  countless  experiments 
that  have  been  made  with  reflected  beams,  no  careful 
measurement  has  ever  suggested  the  slightest  departure 
from  the  law  of  equal  angles,  i  =  r.  And  the  same  may 
be  said  of  Snell's  law  of  refraction.  Of  course  there  is 
a  possible  error  in  all  such  measurements,  for  no  amount 
of  care  can  make  them  absolutely  exact.  A  considerable 
part  of  modern  science  consists  in  estimating  carefully 
the  probable  errors  of  measurement.  To  test  these  laws 
of  reflection  and  refraction,  it  is  necessary  to  measure  cer- 
tain angles,  and  this,  with  the  wonderful  instruments  of 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        121 

to-day,  can  be  done  with  great  nicety,  though  of  course 
not  with  absolute  precision.  With  very  great  care  the 
angles  may  be  measured  accurately  enough  to  insure  the 
correctness  of  refractive  indices  to  six  places  of  decimals; 
but  even  with  the  care  and  skill  necessary  to  insure  this 
degree  of  accuracy,  no  one  has  found  any  departure  from 
Snell's  law  that  was  outside  the  limits  of  the  probable  errors 
of  experiment. 

It  will  have  been  observed  that  these  laws  of  reflection 
and  refraction  are  merely  condensed  statements  of  experi- 
mental facts.  No  theory  is  involved  in  them ;  they  simply 
sum  up  in  a  convenient  form  the  results  of  a  large  number 
of  observations  and  so  serve  one  of  the  great  ends  of  science 
—  to  save  labor  and  relieve  our  memories  of  the  burden  of 
too  many  isolated  facts.  If,  however,  we  are  imbued  with 
the  scientific  spirit,  we  cannot  rest  content  with  such  laws, 
but  must  strive  to  fit  them  in  with  our  other  knowledge 
and  to  get  a  view  of  optics  that  is  comprehensive  enough 
to  take  in  these  laws  and  all  else  within  the  optical  field 
besides.  To  this  end  we  need  a  theory  of  light,  and  for 
about  a  century  there  has  been  little  doubt  as  to  the  gen- 
eral lines  along  which  such  a  theory  must  be  developed. 
We  need  a  wave  theory  of  some  kind,  that  is,  we  must  think 
of  light  as  due  to  a  periodic  disturbance  like  a  wave  propa- 
gated in  a  medium.  Now,  if  we  set  out  with  any  such  wave 
theory,  and  with  the  conception  that  a  wave  travels  with 
a  definite  speed  in  one  medium  (such  as  air),  and  with  a 
different  speed  in  another  (such  as  glass),  we  are  led  simply 
and  inevitably  to  just  these  laws  of  reflection  and  refraction 
of  which  we  have  been  speaking.  These  laws  are  required 
to  secure  continuity  at  the  interface  between  two  media; 
without  them  there  would  be  a  rupture  there  or  a  sudden 


122  LIGHT 

break.  At  present  I  cannot  stop  to  prove  such  a  statement, 
although  it  is  very  easily  proved;  I  must  simply  ask  you 
to  believe  that  it  is  so,  and  that  the  relative  refractive  index 
of  which  we  have  spoken  is  the  ratio  of  the  speeds  of  the 
waves  in  the  two  media  under  consideration. 

As  far,  then,  as  the  mere  directions  of  the  reflected  and 
refracted  rays  are  concerned,  almost  any  wave  theory  will 
account  for  the  facts.  But  other  things  than  these  directions 
must  be  considered.  Suppose  that  you  are  studying  the 
effect  of  waves  that  you  see  running  across  the  surface  of  a 
lake.  You  may  well  want  to  know  more  than  the  mere 
direction  in  which  they  are  moving.  If  you  wish  to  esti- 
mate the  damage  that  the  waves  will  do  when  they  strike 
upon  some  object,  you  will  want  to  know  their  height. 
In  an  ether  wave  which,  according  to  our  theory,  gives  us 
the  sensation  of  light,  each  element  of  the  ether  vibrates  to 
and  fro  about  some  mean  position.  Its  greatest  displace- 
ment from  this  position  corresponds  exactly  to  the  height 
in  a  water  wave,  and  is  technically  known  as  the  amplitude 
of  the  wave.  This  you  will  wish  to  know  if  you  are  to  meas- 
ure the  intensity  of  the  light,  for  it  may  be  proved  that  the 
intensity  depends  on  the  amplitude,  and  is,  in  fact,  propor- 
tional to  the  square  of  this  amplitude.  Another  important 
element  in  a  wave  of  water,  or  of  anything  else,  is  its  phase. 
Watch  two  waves,  similar  in  height  and  shape,  running 
side  by  side  along  the  surface  of  some  water.  The  crest  of 
one  may  always  be  in  line  with  the  crest  of  the  other.  In 
this  case  they  could  be  described  as  being  "in  phase,"  or 
"in  the  same  phase."  More  probably,  however,  the  crest 
of  one  would  lag  somewhat  behind  that  of  the  other.  To 
describe  this  we  should  say  that  there  was  a  "  difference  of 
phase"  between  the  waves,  and  this  difference  might  be 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        123 

a  matter  of  much  import.  (As  a  matter  of  fact,  it  would 
have  great  importance  if  we  came  to  consider  the  effect 
of  combining  the  two  waves,  as  we  shall  see  in  the  next 
lecture  on  Interference.)  What,  then,  does  a  wave  theory  of 
light  tell  us  of  the  amplitude  (or  intensity)  and  the  phase 
of  the  reflected  and  of  the  refracted  beams,  and  how  do 
the  predictions  of  theory  compare  with  the  results  of  obser- 
vation? These  are  very  important  questions.  They  are, 
indeed,  crucial  in  optical  theory,  for  they  enable  us  to  dis- 
tinguish one  wave  theory  from  another,  and  to  say  which 
best  fits  the  facts.  This,  of  course,  settles  the  question  as 
to  which  theory  is  to  be  preferred,  for  the  whole  end  of  a 
scientific  theory  is  to  fit  the  facts ;  if  it  fails  to  do  this,  it  is 
probably  worse  than  useless.  What,  however,  do  we  mean  by 
distinguishing  one  wave  theory  from  another  ?  Any  theory 
of  light  that  endeavors  to  coordinate  its  phenomena  by 
means  of  the  conception  of  a  to-and-fro  motion  propagated 
in  the  ether  may  be  called  a  wave  theory;  but  before  such  a 
theory  can  lead  us  to  precise  results,  we  must  formulate  defi- 
nite ideas  as  to  the  nature  of  the  ether.  Here  there  is  room 
for  difference  of  opinion,  and  so  for  different  wave  theories. 
In  any  case  the  idea  of  an  ether  is  an  abstraction;  it  is  reached 
by  taking  away  certain  properties  of  ordinary  matter  and 
endowing  an  ideal  medium  with  all  that  remains.  Without 
such  a  process  the  ether  could  not  be  thought  of  at  all,  for 
our  mental  conceptions  are  necessarily  derived,  more  or 
less  directly,  from  our  experience.  Such  abstract  ideas 
are  common  enough  in  scientific  and  even  in  ordinary 
discussion.  Thus  we  have  the  idea  of  an  incompressible 
substance.  We  observe  that  air  is  easily  compressed,  that 
bread  resists  compression  more  strongly,  and  that  water 
opposes  with  tremendous  force  any  attempt  to  diminish  its 


124  LIGHT 

volume.  It  is  an  easy  matter  in  thought  to  carry  on  the 
process  until  we  have  abstracted  completely  the  power  of 
yielding  to  compression,  and  so  we  reach  the  abstract  idea 
of  an  incompressible  substance.  If  we  were  interested  in 
considering  the  motion  of  such  a  substance,  we  might  well 
apply  accepted  dynamical  principles  to  aid  us  in  the  dis- 
cussion, and  so  we  might  reason  as  to  its  behavior,  even 
although  it  would  be  impossible  actually  to  point  to  a  sub- 
stance that  was  incompressible.  Again,  we  have  the  idea 
of  a  frictionless  fluid.  We  observe  that  if  w£  pull  a  spoon 
through  treacle,  the  treacle  resists  the  motion,  and  we  have 
to  exercise  a  considerable  force  to  overcome  this  resistance, 
or  friction.  If  we  replace  the  treacle  by  olive  oil,  the  friction 
is  diminished,  while  with  water  it  is  scarcely  perceptible. 
Here,  again,  it  is  not  difficult  to  abstract  the  viscosity,  the 
power  of  opposing  motion  by  friction,  and  so  to  arrive  at  the 
abstract  idea  of  a  frictionless  fluid.  In  this  case,  also,  we 
might  apply  dynamical  principles  to  aid  us  in  discussing  the 
behavior  of  such  a  fluid,  and  we  need  not  be  hampered  in 
that  discussion  by  the  fact  that  no  one  has  ever  presented 
us  with  a  bottle  of  a  frictionless  fluid.  Now  the  ether  that 
is  spoken  of  so  much  in  these  latter  days  in  various 
branches  of  science  is  a  similar  abstraction.  Let  us  begin 
with  ordinary  matter,  a  piece  of  steel  or  jelly,  say.  It  has  a 
definite  density,  and  definite  elastic  constants  which  meas- 
ure its  powers  of  resistance.  It  resists  a  change  of  volume ; 
it  requires  force  to  compress  or  expand  it.  It  resists  at- 
tempts to  twist  it  and  change  its  shape.  Such  powers  of 
resistance  can  be  measured  on  a  definite  scale  and  expressed 
numerically  by  means  of  such  elastic  constants  as  com- 
pressibility and  torsional  rigidity.  It  seems  natural  in  a 
wave  theory  of  light  to  begin  with  an  ether  that  has  all 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        125 

these  powers,  and  to  see  if,  by  a  proper  choice  of  the  con- 
stants representing  density,  compressibility,  and  rigidity, 
it  is  possible  to  account  for  the  phenomena  of  light.  This 
is  the  famous  elastic  solid  theory  of  light.  If  a  disturbance 
is  set  up  in  a  medium  such  as  has  been  described,  it  is  easy 
to  show  that  waves  will  be  propagated  with  a  speed  that 
will  depend  on  the  magnitude  of  the  elastic  constants. 
Moreover,  in  passing  from  one  medium  to  another  with  dif- 
ferent elastic  constants,  reflected  and  refracted  waves  will 
be  set  up,  and,  as  has  been  indicated  already,  the  directions 
of  these  will  correspond  exactly  to  those  laid  down  by  the 
laws  of  reflection  and  refraction  that  have  already  been 
formulated  and  have  been  fully  verified  by  experiment. 
It  would  thus  appear  that  we  are  on  the  right  track;  but 
when  we  come  to  look  carefully  at  the  other  features  of  the 
waves,  their  amplitudes  and  phases,  we  begin  to  encounter 
difficulties.  There  are  other  difficulties  that  I  need  not 
refer  to ;  it  will  be  sufficient  to  say  that  the  only  successful 
way  of  overcoming  them  all  is  to  abstract  something  from 
our  ordinary  elastic  medium.  We  have  too  much  cargo  and 
must  lighten  the  ship.  Let  us  throw  over  all  power  of 
resisting  change  of  shape,  except  the  power  of  resisting  a 
twist.  The  medium  so  obtained  will  possess  the  mobility 
of  a  fluid  with  some  of  the  rigidity  of  a  solid.  As  it  does  not 
resist  a  mere  change  of  shape,  it  will  allow  bodies  to  move 
freely  through  it  like  a  fluid;  but  it  objects  to  twisting  of 
its  elements,  and  so  has  rigidity.  A  fluid  like  water,  with 
a  number  of  little  gyrostats  spinning  in  it,  and  by  their 
momentum  opposing  any  change  of  spin,  might  serve  as 
a  rough  model  to  bring  to  mind  the  peculiar  properties  of 
this  " rotationally  elastic"  ether.  It  might  be  impossible 
to  construct  this  model,  but  there  is  no  great  difficulty  in 


126  LIGHT 

conceiving  of  such  a  medium  by  the  process  of  abstraction 
and  of  reasoning  as  to  its  behavior  in  obedience  to  general 
dynamical  laws.  Such  a  medium,  if  disturbed,  will  transmit 
the  disturbance  as  a  wave  (i.e.  a  periodic  displacement),  and 
this  wave  will  not  be  of  the  longitudinal  type,  but  of  the 
transverse  kind  that  the  phenomenon  of  polarization  demands 
from  any  theory  of  light.  The  speed  with  which  the  wave 
travels  will  depend  on  the  rigidity  and  the  density  of  the  ether, 
and  the  ratio  of  the  constants  representing  these  quantities 
must  be  chosen  so  as  to  fit  in  with  the  observed  value  of  the 
speed  of  light  in  vacuo  where  there  is  nothing  but  ether 
to  affect  the  speed.  The  presence  of  matter  will  modify 
the  effective  rigidity,  so  that  a  wave  will  travel  with  a  dif- 
ferent speed  in  water  or  glass  than  in  vacuo.  In  passing 
from  one  of  these  media  to  the  other,  there  will  be  reflection 
and  refraction,  and  provided  that  we  assume  that  there  is 
no  discontinuity  of  motion  at  the  interface,  no  rupture  at 
the  surface  of  separation,  the  general  principles  of  dynamics 
will  enable  us  to  calculate  not  only  the  directions  of  the 
reflected  and  refracted  waves,  but  also  their  amplitudes 
and  phases.  When  this  is  done,  it  becomes  at  once  evident 
that  the  condition  of  the  reflected  and  refracted  waves  must 
depend  on  the  state  of  polarization,  as  well  as  on  the  direc- 
tion, of  the  incident  beam.  Two  important  cases  present 
themselves :  in  one  the  light  is  polarized  parallel  to  the  plane 
of  incidence,  and  in  the  other  at  right  angles  to  this  plane 
—  these  cases  being  specially  important,  as  the  details  of  all 
other  cases  can  be  immediately  deduced  from  a  considera- 
tion of  these  two.  Then  it  also  appears,  as  might  be  ex- 
pected, that  the  results  depend  on  the  nature  of  the  tran- 
sition from  one  medium  to  the  other,  from  air  to  water,  say. 
In  any  case,  actually  presented  in  an  experiment,  this  tran- 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        127 

sition  may  be  absolutely  sudden,  or  it  may  be  more  or  less 
gradual.  Such  a  question  cannot  be  decided  offhand;  to 
the  eye  the  transition  may  look  quite  sudden,  but  this 
effect  may  be  due  to  imperfections  of  our  vision,  and  if  we 
could  see  things  at  close  enough  range,  the  idea  of  an  abso- 
lutely sudden  transition  might  appear  illusory.  However, 
the  hypothesis  of  a  sudden  transition  is  probably  the  natural 
one  with  which  to  begin,  and  it  was  on  this  hypothesis  that 
formulae  from  which  to  calculate  all  the  details  of  the  re- 
flected and  refracted  waves  were  first  obtained.  In  the 
present  course  I  have  promised  to  eschew  mathematics 
as  much  as  possible,  so  that  here  we  must  be  content  with 
a  graphical  representation  of  the  formulae.  Instead  of 
looking  at  all  the  details,  let  us  for  a  time  concentrate  our 
attention  on  a  single  one,  the  intensity  of  the  reflected  beam 
—  a  quantity,  as  has  been  remarked,  that  is  proportional 
to  the  square  of  the  amplitude  of  the  reflected  wave.  In 
Fig.  29  the  curves  marked  R  and  R'  represent  the  percent- 
age of  the  incident  light  reflected  from  glass,  whose  refrac- 
tive index  is  /*  =  1.52,  at  different  angles  of  incidence  i. 
The  different  angles  of  incidence  are  indicated  by  distances 
measured  across  the  page,  and  the  corresponding  percent- 
age of  reflected  light  by  distances  at  right  angles  to  this. 
Both  curves  represent  the  formulae  obtained  from  theory  in 
the  manner  just  indicated,  R'  dealing  with  light  polarized 
parallel  to  the  plane  of  incidence,  and  R  perpendicular 
thereto.  It  is  specially  worthy  of  remark  that  for  the  latter 
case  the  intensity  begins  to  diminish  as  the  angle  of  inci- 
dence (i)  increases,  that  it  goes  to  zero  at  the  point  marked 
P,  and  then  rapidly  rises.  The  theory  indicates  that  the 
position  of  the  point  P  is  determined  by  the  simple  formula 
tan  i  =  /*.  At  this  angle  none  of  the  light  that  is  polarized 


128 


LIGHT 


perpendicularly  to  the  plane  of  incidence  is  reflected,  so 
that  all  the  light  that  can  be  reflected  at  that  angle  is  po- 
larized parallel  to  the  plane  of  incidence.  This  indicates 


100 

1 

90 
80 
70 
60 

I 

I 

1 

' 

/ 

1 

\ 

I 

I 

[    I 

40 

/ 

/ 

/ 

1 

J 

' 

1 

L 

J 

y 

1 

/ 

j 

Percentage  i 

1  """  O  C 

x 

R/ 

X 

/ 

•••• 

—    - 

- 

- 

• 
• 

- 

—  —  ' 
- 

-~— 

—   — 

—^^ 

- 

/ 

0—  * 

10°          20°          30°           40°          50°  P     60°           70°          80°          90° 

Angle  of  Incidence  (t) 


FIG.  29 


that  by  simple  reflection  we  have  a  means  of  producing 
plane  polarized  light.  We  have  merely  to  arrange  that 
light  should  fall  on  a  reflecting  surface  at  the  proper  angle. 
This  angle  is  given  by  the  formula  tan  i  =  p,  and  is  called 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        129 


the  polarizing  angle.  It  is  just  about  a  century  since  Malus 
discovered  that  light  could  be  polarized  by  reflection,  and  a 
few  years  later  Brewster  deduced  from  a  series  of  experi- 
ments that  the  polarizing  angle  was  given  by  the  formula 
tan  i  =  p.  The  following  table  shows  how  the  values  of 
the  polarizing  angles  of  different  substances,  calculated 
from  the  theoretical  formula  tan  i  =  /*,  agree  or  disagree 
with  the  angles  actually  observed :  — 


i  (theory) 

53°  7' 

53°  18' 

55°  33' 

55°  37' 

58°  13' 

58°  36' 

i  (experiment)  . 

53°  7' 

53°  18' 

55°  33' 

55°  37' 

58°  12' 

58°  36' 

i  (theory)   .  . 

59°  41' 

60°  30' 

63°  33' 

67°  7' 

67°  32' 

67°  40' 

i  (experiment)  . 

59°  44' 

60°  30' 

63°  34' 

67°  6' 

67°  26' 

67°  30' 

It  will  be  seen  that  the  agreement  is  very  close,  but  not 
perfect,  and  we  should  find  results  of  the  same  character 
if  we  compared  the  theoretical  and  observed  values  of  the 
intensity  of  the  reflected  light,  and,  what  are  much  more 
readily  measured  with  precision,  certain  phase  relations.  In 
all  cases  the  theory  fits  the  facts  very  nearly,  but  not  ex- 
actly. We  find,  however,  that  all  these  minute  discrep- 
ancies disappear  when  we  abandon  the  hypothesis  of  an 
abrupt  transition  from  one  medium  to  another.  A  com- 
parison of  theory  and  experiment  then  gives  us  the  means  of 
estimating  approximately  the  thickness  of  the  surface  layer 
within  which  the  transition  takes  place.  We  find  in  many 
cases  that  it  is  less  than  one-hundredth  of  a  wave  length,  and 
how  extremely  short  that  is  for  ordinary  light  will  be  made 
apparent  in  a  later  lecture.  Let  us  see  how  well  our  theory 
fits  the  facts  when  we  take  into  account  the  influence  of 


130 


LIGHT 


this  transition  layer.  We  shall  consider  first  the  intensity 
of  the  reflected  light,  although  the  intensity  cannot  be  meas- 
ured so  accurately  as  most  of  the  other  features  with  which 
we  have  to  deal.  It  is  true  that  there  has  been  a  great  im- 
provement in  photometric  processes  of  recent  years,  but 
these  are  still  far  from  the  stage  of  precision  that  has  been 
attained  in  other  departments  of  optics.  The  following 
table  gives  the  percentage  of  the  light  reflected  at  different 
angles  of  incidence  (i),  calculated  from  theory  for  the  case 
of  glass,  and  compares  the  results  with  the  most  careful 
observations  of  the  amount  of  light  actually  reflected :  — 


i 

0 

10° 

20° 

30° 

40° 

Percentage  Reflected  (theory)    .    . 

3.78 

3.78 

3.90 

3.92 

4.39 

Percentage  Reflected  (experiment) 

3.78 

3.78 

3.77 

3.92 

4.37 

i 

50° 

60° 

65° 

70° 

Percentage  Reflected  (theory)     .    . 

5.37 

8.31 

11.28 

16.12 

Percentage  Reflected  (experiment) 

5.53 

8.34 

11.16 

16.04 

Some  of  you,  who  find  numbers  distasteful  or  hard  to  com- 
prehend, may  prefer  to  see  these  results  exhibited  in  a  form 
that  appeals  to  the  eye.  For  this  purpose  they  are  ex- 
hibited graphically  in  Fig.  30.  As  we  shall  have  quite  a 
number  of  similar  figures  before  our  course  is  run,  it  may 
be  well  to  adopt  a  uniform  mode  of  presentation  and  explain 
it  once  for  all  here.  You  should  bear  in  mind,  then,  that 
in  all  such  figures,  the  continuous  curve  corresponds  to  the 
predictions  of  theory,  while  the  crosses  indicate  the  results 
of  actual  experiment.  Thus  the  agreement  or  disagreement 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        131 


between  theory  and  observation  is  measured  by  the  degree 
of  closeness  with  which  the  crosses  lie  along  the  continuous 
curve.  In  this  case  it  will  be  observed  that  the  agreement 


16 


14 


12 


10 


,.       10°  20° 

Angle  of  Incidence  (i) 


40° 


60° 


Fio.  30 


is  very  close,  especially  in  the  region  where  the  incidence  is 
small,  in  which  accurate  measurements  are  most  easily  made. 
An  inspection  of  the  figure  will  show  that,  in  the  case  of  the 
most  marked  disagreement,  it  is  more  probable  that  the  meas- 
ure of  intensity  was  rather  too  high,  or  too  low,  than  that 


132 


LIGHT 


the  theory  is  in  error.  In  nearly  all  cases  the  differences 
between  theory  and  observation  are  well  within  the  limits 
of  the  probable  errors  of  experiment. 

So  much  for  the  intensity  of  the  reflected  light.  Next, 
let  us  suppose  that  matters  are  so  arranged  that  the  in- 
cident light  has  equal  intensities  when  polarized  parallel 
and  perpendicularly  to  the  plane  of  incidence,  and  let  us 
measure  the  ratio  of  the  intensity  of  the  reflected  light  that 
is  polarized  perpendicularly  to  the  plane  of  incidence  to 
that  of  the  reflected  light  that  is  polarized  parallel  to  this 
plane.  The  measurement  of  this  ratio  can  be  made  far 
more  accurately  than  that  of  the  intensity  of  any  light.  Its 
value  can  be  obtained  without  any  photometric  processes 
at  all,  simply  by  ascertaining  the  position  of  the  plane  of 
polarization  of  the  reflected  light,  and  the  measurement 
of  the  angle  determining  this  position  is  an  operation  that 
can  be  performed  with  great  delicacy.  The  table  that  fol- 
lows gives  us  the  means  of  comparing  the  values  of  this  ratio 
in  the  case  of  reflection  from  diamond  at  various  angles  of 
incidence  and  of  estimating  the  degree  of  accuracy  with 
which  the  theory  fits  the  facts :  — 


i 

60° 

61° 

62° 

63° 

64° 

65° 

Ratio  (theory)      .     . 

.0421 

.0324 

0234 

.0166 

.0104 

.0056 

Ratio  (experiment)  . 

.0420 

.0312 

.0213 

.0178 

.0102 

.0057 

i 

66° 

67° 

67°  30' 

68° 

68°  30' 

69° 

Ratio  (theory)      .     . 

.0028 

.0009 

.0006 

.0007 

.0013 

.0020 

Ratio  (experiment)  . 

.0030 

.0009 

.0006 

.0007 

.0013 

.0026 

i 

7O° 

71° 

72° 

73° 

74° 

75°  . 

Ratio  (theory)      .    . 

.0049 

.0103 

.0177 

.0275 

.0399 

.0552 

Ratio  (experiment)  . 

.0054 

.0106 

.0184 

.0296 

.0469 

.0576 

Qi-     j  nc.  » 

UNIVERSITY  j 
OF  / 


OF  REFLECTION  AND  REFRACTION       133 


The  graphical  representation  of  these  results  is  exhibited 
in  Fig.  31,  and  from  either  the  figure  or  the  table  it  will  be 
seen  that  the  agreement  between  theory  and  observation  is 
extremely  satisfactory. 

Another  quantity  that  is  capable  of  very  accurate  meas- 
urement is  the  difference  of  phase  between  the  two  reflected 


0.05 


\ 


0.04 


0.03 


\ 


\ 


0.02 


0.01 


waves  when  one  is  polarized  parallel  and  the  other  per- 
pendicularly to  the  plane  of  incidence.  The  results  for 
diamond  are  shown  in  Fig.  32,  the  difference  of  phase  being 
expressed  as  a  decimal  fraction  of  a  wave  length,  so  that  for 
a  difference  marked  0.5  one  wave  is  half  a  wave  length  be- 
hind the  other,  and  thus  the  crest  of  the  first  is  in  line  with 
the  hollow  of  the  second.  It  was  pointed  out  earlier  in  this 
lecture  that,  on  the  theory  of  an  absolutely  abrupt  transi- 
tion from  one  medium  to  another,  the  polarizing  angle 
would  be  given  by  the  formula  tan  i  =  /*,  and  a  table  was 


134 


LIGHT 


made  out  which  showed  that  this  is  very  nearly  true  for 
most  of  the  substances  referred  to.  The  examination  of 
the  influence  of  a  thin  surface  layer  of  transition  on  the 
position  of  the  polarizing  angle  shows  that  the  layer  should 
affect  this  angle  very  slightly,  and  that  it  might  either  in- 
crease or  decrease  it,  according  to  the  nature  of  the  layer. 


0.5 


0.4 


0.3 


It 


^          60°  62° 

.Angle  of  Incidence  (i) 


64°     66°     68° 
FIG.  32 


70° 


72° 


74° 


In  the  case  of  a  certain  specimen  of  glass,  for  which  the 
theory  of  the  transition  layer  predicted  a  polarizing  angle  of 
56°  23'  38",  the  mean  of  a  most  careful  series  of  experiments 
fixed  this  angle  at  56°  23'  30". 

Theory  also  shows  that  if  the  first  of  the  two  media  in 
contact  with  one  another  have  a  higher  refractive  index 
than  the  second,  the  whole  of  the  light  will  be  reflected 
when  the  angle  of  incidence  is  greater  than  the  critical  angle. 
This  is  the  phenomenon  of  total  reflection  already  referred 
to,  and  here,  as  elsewhere,  the  agreement  between  theory 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        135 


and  observation  is  as  close  as  could  be  desired.  The 
following  table  and  Fig.  33  set  out  a  comparison  between 
theory  and  experiment  for  the  difference  of  phase  (A) 
between  two  waves  that  are  totally  reflected,  one  being 


Difference^/  Phase 

—  0-*  0  p 

L.w  k.  o« 

\ 

S 

X, 

1  —  j 

»-  .— 

~  -t 

- 

—  ^ 

•i  i     i 

H1 

•      H 

^     - 

tft°x         40°          42°          44»           46°          48°           B0°          52°          64°          6 
Angle  of  Incidence  (i) 
FIG.  33 

*>J 

polarized  parallel  and  the  other  perpendicular  to  the 
plane  of  incidence.  The  differences  of  phase  are  expressed 
as  decimal  fractions  of  the  wave  length,  and,  as  before,  i 
denotes  the  angle  of  incidence.  The  substance  dealt  with 
experimentally  had  a  refractive  index,  ^  =  1.619,  and  a 
critical  angle  of  38°  9'. 


i 

38°  13' 

39°  58' 

41°  59' 

44°  3' 

46°  4' 

A  (theory)    . 

.488 

.457 

.379 

.364 

.358 

A  (experiment)     .     .     . 

.489 

.457 

.377 

.364 

.359 

i 

47°  54' 

49°  58' 

51°  57' 

53°  58' 

55°  57' 

A  (theory)   ... 

356 

356 

360 

363 

368 

A  (experiment)     .     .     . 

.356 

.357 

.360 

.363 

.365 

All  these  tables  and  figures  have  reference  to  reflection 
from  transparent,  non-crystalline  substances.  If  the  re- 
flector be  a  crystal,  or  if  it  be  more  or  less  opaque,  theory 


136 


LIGHT 


and  experiment  agree  in  showing  that  the  laws  of  reflec- 
tion may  be  considerably  modified.  The  phenomena  with 
crystals  will  be  dealt  with  in  a  later  lecture,  but  we  shall 


100 
90 
80 
70 
60 
60 
#> 

*!»    n/\ 

J 

H 

2  II 

/ 

/ 

/ 

/ 

S 

/ 

R 

S* 

^ 

^ 

^ 

? 

•M 

—    - 
—  .  , 

_  — 
—  .  — 

_  — 


_^-— 
—  -~^. 

ft 

"*""*• 

^ 

^v^ 

T?~ 

* 

****. 

>^ 

\ 

/ 

\ 

n 

Percentage  Reflectet 

m  ^g  8  % 

s 

**•  —  j, 

,/ 

= 

)  „    10°           20°           30°          40°          60°           60°           70°          80°          90° 
Angle  of  Incidence  (i) 

FIG.  34 

not  have  time  for  more  than  a  passing  reference  to  the  laws 
of  reflection  from  opaque  substances,  such  as  metals.  In 
this  case  what  corresponds  to  the  refracted  wave  is  absorbed 
by  the  metal,  but  theory  enables  us  to  predict  all  the  details 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        137 

of  the  reflected  beam.  The  laws  are  more  complex,  but 
the  general  character  of  the  results  has  some  resemblance 
to  that  for  transparent  reflectors.  This  will  be  made  evi- 
dent by  a  comparison  of  Figs.  29  and  34,  which  represent 
corresponding  quantities  for  glass  and  steel.  It  will  be 


0.5 

n  4 

/ 

/ 

/ 

0.3 
0.2 
^0.1' 

/ 

/ 

x 

7 

/ 

/ 

/ 

x 

^^ 

^ 

f 

.• 

J 

—  -^ 

30°              40°              50°              60°              70°              80°             91 
—  —^  Angle  of  Incidence  (i) 

FIG.  35 

observed  that  in  both  cases  for  light  polarized  parallel  to 
the  plane  of  incidence  the  intensity  of  the  reflected  beam 
increases  steadily  with  the  incidence.  With  light  polarized 
perpendicularly  to  the  plane  of  incidence,  the  intensity 
in  both  cases  begins  by  diminishing,  reaches  a  minimum, 
and  then  increases  rapidly.  The  main  difference  is  that 
the  amount  of  light  reflected  at  normal  incidence  is  very 
much  greater  for  the  metal  than  for  the  transparent  sub- 
stance, and  that  even  at  the  angle  where  the  reflection  from 
the  metal  is  a  minimum  (called  the  quad-polarizing  angle 
from  its  resemblance  to  the  polarizing  angle  of  a  transparent 


138 


LIGHT 


medium),  there  is  still  a  considerable  quantity  of  light  re- 
flected from  the  metallic  surface.  The  difference  of  phase 
between  the  two  reflected  waves  is  represented  graphically 
in  Fig.  35  for  the  case  of  reflection  from  gold.  This  figure 
should  be  compared  with  Fig.  32,  which  is  the  corresponding 
figure  for  the  case  of  reflection  from  a  transparent  substance. 
It  will  be  seen  that  in  all  cases  the  crosses  lie  closely  along 
the  curves,  indicating  on  all  points  an  excellent  agreement 
between  theory  and  observation.  The  numbers  corre- 
sponding to  these  figures  are  set  out  in  the  following 
table:  — 


i 

R 

(THEORY) 

R 

(EXPERIMENT) 

R' 

(THEOBY) 

R' 

(EXPERIMENT) 

A 
(THEORY) 

A 
(EXPERIMENT) 

30° 

50.5 

50.1 

60.4 

60.7 

.028 

.032 

40° 

46.5 

46.2 

64.0 

64.2 

.052 

.056 

50° 

41.0 

41.0 

68.9 

69.4 

.088 

.088 

60° 

33.9 

34.1 

74.8 

74.5 

.135 

.130 

70° 

26.7 

26.5 

82.1 

82.3 

.211 

.210 

75° 

25.4 

25.5 

86.1 

86.1 

.265 

.265 

80° 

29.5 

27.5 

90.4 

90.3 

.331 

.324 

I  hope  that  by  this  time  enough  has  been  said  to  show  you 
that  modern  optical  theory  gives  a  completely  satisfactory 
account  of  reflection  and  refraction,  telling  us  all  that  we 
can  want  to  know  with  the  utmost  precision,  and  agreeing 
in  its  predictions  on  every  point  with  the  most  accurate 
measurements  of  the  best  experimenters.  We  may  thus 
feel  that  we  have  our  feet  on  solid  ground  when  we  set  out 
to  apply  this  theory  to  aid  us  in  the  solution  of  any  problem 
that  may  present  itself.  In  the  time  that  remains  of  this 
lecture  I  wish  to  speak  mainly  of  the  application  of  the 


THE  LAWS  OF  REFLECTION  AND  REFRACTION      139 

laws  of  reflection  and  refraction  to  the  design  and  con- 
struction of  optical  instruments.  Clearly,  if  I  am  to  do  this 
at  all  effectively,  I  must  limit  myself  strictly.  The  number 
and  variety  of  optical  instruments  is  enormous,  and  it 
requires  not  a  little  thinking  to  suggest  many  instruments 
of  great  precision  that  do  not  involve  some  optical  principle. 
Optics  has  been  called  the  " directing  science"  of  modern 
times,  because  the  principles  that  have  been  developed  in 
its  study  have  formed  the  basis  of  many  of  the  most  far- 
reaching  speculations  in  modern  science.  It  deserves  the 
name  perhaps  even  more  truly  for  another  reason.  The 
advancement  of  science  depends  largely  on  the  precision 
with  which  its  researches  can  be  conducted.  Optical  prin- 
ciples enter  into  nearly  all  instruments  of  precision,  and  thus 
the  whole  army  of  science  is  interested  in  these  principles, 
and  should  realize  that  it  is  under  a  deep  obligation  to  those 
men  who  have  established  them  so  firmly. 

The  laws  of  reflection  and  refraction  that  are  most  fre- 
quently made  use  of  in  the  design  of  optical  instruments 
are  those  simpler  ones  that  deal  with  the  directions  of  the 
rays.  These  laws  have  already  been  stated  and  discussed, 
but  perhaps  you  will  bear  with  me  if  I  call  your  attention  to 
a  different  mode  in  which  they  may  be  presented.  We  have 
seen  that  if  a  ray  of  light  proceeding  from  A  (Fig.  36), 
strike  a  surface  BC  so  as  to  be  reflected  to  E,  the  lines 
AB  and  BE  will  be  equally  inclined  to  the  reflecting  surface. 
Suppose,  now,  that  we  endow  a  ray  of  light  with  intelligence, 
and  set  it  this  problem:  to  start  from  A,  strike  the  re- 
flecting surface  somewhere,  and  be  reflected  to  E,  and  to 
choose  its  path  so  that  it  will  reach  E  as  quickly  as  possible. 
If  you  have  any  skill  in  elementary  geometry,  you  will 
be  able  to  prove  that  B,  the  point  of  striking  the  reflector, 


140  LIGHT 

must  be  chosen  so  that  AB  and  BE  make  equal  angles  with 
BC  ;  in  other  words,  the  law  of  reflection  must  be  obeyed. 
Similarly,  if  you  take  the  corresponding  problem  in  re- 
fraction, and  ask  the  ray  to  set  out  from  A  (Fig.  36),  be 
refracted  into  another  medium,  and  reach  a  point  E  in  the 
shortest  possible  time,  you  will  find  that  here,  again,  the  law 
of  refraction  will  have  to  be  obeyed.  In  both  cases  you 
can  prove  the  statements  by  showing  that  the  time  of  pass- 


BQ 

Reflection 


FIG.  36 

age  along  ABE  is  less  than  that  along  any  other  route,  such 
as  ACE,  and  in  the  second  problem  you  must  bear  in  mind 
that  the  velocity  in  any  medium  is  inversely  proportional  to 
the  absolute  refractive  index  of  that  medium.  It  would  thus 
appear  that  rays  of  light  always  try  to  reach  their  destina- 
tion as  quickly  as  possible  —  a  curious  principle.  It  would 
be  very  interesting  to  trace  its  development,  its  limitations, 
and  its  applications  to  a  variety  of  problems.  However, 
there  is  no  time  for  this  now,  nor  can  we  do  more  than  refer 
to  the  fact  that  this  principle  has  suggested  to  science  a  much 
more  far-reaching  law,  what  is  known  as  the  Principle  of 
Least  Action,  the  greatest  generalization  of  modern  science. 
The  principle  was  first  enunciated  a  century  and  a  half 
ago  by  Maupertuis,  then  president  of  the  Berlin  Academy. 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        141 

He  laid  it  down  because,  in  his  judgment,  it  was  eminently 
in  accord  with  the  wisdom  of  the  Creator.  More  modern 
men  of  science  do  not  often  feel  so  confident  about  sharing 
in  the  secrets  of  Providence;  but  they  find  the  principle 
none  the  less  useful  in  making  for  the  great  end  they  have  in 
view  —  to  comprehend  all  knowledge  in  a  single  law. 

To  return  to  the  application  of  the  laws  of  reflection  and 
refraction,  I  repeat  that  it  is  necessary  to  limit  myself  very 
strictly.  You  will  find  large  treatises  on  Geometrical  Optics, 
which  are  taken  up  wholly  with  applications  of  the  simplest 
of  these  laws,  and  whole  books  that  treat  of  their  bearing 
on  the  construction  of  special  instruments.  In  the  short 
time  that  remains  in  this  lecture,  it  is  obviously  impossible 
to  cover  so  much  ground.  I  must  select  a  single  illustrative 
example,  and  deal  with  one  optical  instrument,  and  even 
with  that  in  a  very  cursory  manner.  What  is  this  instru- 
ment to  be?  The  one  most  generally  interesting  would 
be  the  human  eye,  for  there  we  have  an  optical  instrument 
that  we  must  all  use.  Apart  from  that,  it  is  extremely 
interesting  merely  as  an  illustration  of  optical  principles. 
It  is  truly  a  wonderful  instrument  or  combination  of  instru- 
ments. It  is  at  the  same  time  a  microscope,  a  telescope, 
a  range-finder,  a  stereoscope,  a  photometer,  a  kinemato- 
graph,  and  an  autochrome  camera.  An  instrument  that 
serves  so  many  purposes  can  scarcely  be  expected  to  be 
free  from  imperfections,  and  the  eye  is  not  without  its 
defects.  At  the  same  time,  to  the  student  of  optics  it  is 
as  interesting  in  its  defects  as  in  its  strength.  How  to 
cure  these  defects  or  how  to  minimize  their  evil  conse- 
quences is  a  human  problem  that  requires  for  its  successful 
solution  an  intimate  knowledge  of  the  scientific  principles 
here  discussed.  However,  the  eye  is  not  an  instrument 


142  LIGHT 

that  we  have  completely  under  our  control ;  at  the  best  we 
can  supplement  it.  So  it  will  be  better  for  our  present  pur- 
pose to  take  another  instrument,  where  there  are  no  such 
limitations  on  our  actions,  and  endeavor  to  indicate  how 
our  knowledge  of  the  laws  of  light  may  be  employed  to 
make  it  as  effective  as  possible.  To  this  end,  let  us  select 
the  Astronomical  Telescope,  the  purpose  of  which  is  simple 
and  well  known,  —  to  enable  us  to  see  distant  objects  as 
clearly  as  possible,  and  in  some  cases  to  photograph  their 
details  or  their  relative  positions. 

I  need  not  spend  time  in  emphasizing  the  fundamental 
idea,  which  is  to  get  an  image  of  the  object  near  at  hand, 
and  look  at  this  image  through  a  magnifier.  You  are  all 
doubtless  quite  familiar  with  the  idea  of  the  image  of  an 
object.  You  can  obtain  this  by  reflection  from  a  mirror 
which  is  either  plane  or  curved.  The  plane  mirror  is  the 
only  perfect  optical  instrument,  in  the  sense  that  it  forms 
an  image  that  is  absolutely  faithful  to  the  original,  free 
from  all  distortion  or  other  defects.  A  curved  reflector, 
as  you  know,  produces  a  certain  amount  of  distortion, 
which  is  very  marked  if  the  object  be  a  large  one,  such  as 
the  human  figure.  You  can  also  get  an  image  by  refraction, 
as  with  a  pair  of  spectacles,  a  hand  magnifier,  or  a  photo- 
graphic lens  —  with  one  or  other  of  which  every  one  is 
more  or  less  familiar.  However,  although  the  fact  of  an 
image  being  formed  in  some  such  way  is  well  known,  you 
may  not  have  thought  of  the  mode  in  which  this  image  is 
produced,  or  of  the  bearing  of  optical  principles  upon  its 
formation.  Here  we  have  time  only  for  the  briefest  out- 
line. The  fundamental  principle,  as  usually  stated,  is  that 
the  image  of  a  point  is  a  point.  Each  point  of  an  object 
has  its  image,  and  the  whole  collection  of  such  points  forms 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        143 

a  picture  more  or  less  like  the  original.  Is  it  true,  however, 
that  the  image  of  a  point  is  a  point  ?  Yes,  absolutely  so, 
if  the  reflector  be  a  plane  mirror ;  but  not  so  for  any  other 
case.  In  all  such  cases,  if  we  take  a  series  of  points  in  the 
object,  the  rays  from  any  one  of  them  will,  in  general,  after 
reflection  or  refraction,  or  both,  at  best  pass  only  approxi- 
mately through  a  corresponding  point  in  the  image.  They 
may  all  pass  very  near  indeed  to  this  point  in  the  image, 
but  again,  many  of  them  may  pass  some  distance  away, 
and  the  clearness  of  the  image  will  depend  on  how  close  to 
a  point  the  rays  from  any  point  of  the  object  converge. 
If  we  follow  out  the  consequences  of  the  laws  of  reflection 
and  refraction,  we  find  that  the  rays  from  a  point  converge 
more  nearly  to  some  other  point  if  they  all  strike  the  reflect- 
ing or  refracting  surfaces  very  nearly  at  right  angles  than  if 
they  strike  it  at  oblique  and  widely  varying  angles.  The 
latter,  at  best,  will  give  a  blurred  image;  the  former  will 
make  for  clearness.  Hence,  in  our  telescope  we  must  ar- 
range that  all  the  reflecting  and  refracting  surfaces  are 
"square  on"  to  the  impinging  rays,  and  we  must  choose  the 
form  of  these  surfaces  so  that  a  slight  departure  from  the 
perfect  square  will  introduce  as  little  indistinctness  as 
possible. 

In  the  case  of  a  reflecting  telescope  the  form  of  the  re- 
flecting surface  is  easily  determined.  The  telescope  being 
used  for  astronomical  purposes,  the  incident  rays  come 
from  extremely  distant  points,  so  that  we  have  practically 
to  deal  with  a  series  of  parallel  rays  striking  the  reflector. 
It  is  a  simple  problem  of  geometry  to  prove  under  such 
circumstances  that  the  form  of  reflector  that  will  give  the 
clearest  image  is  a  paraboloid  —  the  surface  formed  by  re- 
volving a  parabola  about  its  axis.  Figure  37  represents  a 


144 


LIGHT 


portion  of  a  parabola  of  which  AX  is  the  axis,  S  the 
focus,  AS  the  focal  length,  and  BE'  the  aperture.  The 
geometrical  property  of  the  parabola,  which  makes  it 

useful    for    this 

B  optical  purpose, 

is  that  if  P  be 
any  point  on  the 
curve,  and  PR 
be  drawn  paral- 
lel to  the  axis, 
then  the  lines 
SP  and  PR 
make  equal 
angles  with  PG, 
which  is  at  right 
angles  to  the 
curve  at  P. 
Hence  a  ray  of 
light  that  comes 
from  a  distant 
point  in  the  di- 
rection PR  will 
be  reflected  to 
the  focus  S, 
wherever  be  the 
point  P. 

So  much  for 
the  form  of  the 

reflector;  what  next  as  to  its  material?  We  want  to 
have  the  image  as  bright  as  possible,  so  we  must  have  a 
surface  with  a  high  reflecting  power.  Theory  and  ob- 
servation agree  in  indicating  some  of  the  metals  as  the 


FIG.  37 


THE  LAWS  OF  REFLECTION  AND  REFRACTION       145 

best  reflectors.  In  the  earlier  reflectors  speculum  metal 
was  commonly  employed  as  being  a  fairly  good  re- 
flector and  not  too  expensive.  Silver,  however,  is  a 
much  better  reflector,  and  any  objections  to  its  use 
have  been  overcome  by  the  discovery  in  recent  times  of 
thoroughly  satisfactory  methods  of  depositing  it  chemically 
upon  glass.  The  thin  film  of  silver  is  not  expensive,  and 
the  glass  supporting  it,  if  carefully  made,  is  fairly  rigid,  and 
so  not  very  easily  distorted.  Freedom  from  distortion  is 
extremely  important  where  good  results  are  required,  for  a 
slight  change  from  the  paraboloidal  form  will  give  different 
images  in  different  parts  of  the  reflector  and  a  consequent 
blur.  In  fact,  in  the  best  modern  reflectors,  the  greatest 
care  is  taken  to  preserve  their  form ;  they  are  kept  as  free 
as  possible  from  changes  of  temperature,  and  the  system 
of  support  is  planned  with  the  utmost  thoroughness.  It 
was  mainly  through  lack  of  such  precautions  that  the  great 
reflectors  of  the  past  proved,  in  many  ways,  so  disappoint- 
ing. 

Consider  next  the  problem  of  the  size  of  the  reflector. 
What  is  to  be  its  aperture  BB',  and  its  focal  length  AS  ? 
A  considerable  increase  in  aperture  will  make  the  instru- 
ment more  cumbrous  and  greatly  add  to  its  cost.  Its 
countera vailing  advantages  are  mainly  two.  In  the  first 
place,  a  larger  aperture  collects  more  light,  and  so  gives 
a  brighter  image.  This  may  be  a  matter  of  great  im- 
portance, if  we  wish  to  see  or  to  photograph  very  faint 
objects.  The  brightness  of  the  image  depends  upon  the 
area  of  the  aperture,  and  is  therefore  proportional  to  the 
square  of  the  diameter  BB'.  Thus,  if  BB'  be  doubled, 
the  brightness  of  the  image  will  be  increased  fourfold. 
The  second  important  advantage  of  a  large  aperture 


146  LIGHT 

will  be  more  fully  appreciated  after  we  have  dealt  with 
Diffraction.  In  the  lecture  on  that  subject  it  will  be  shown 
that  the  image  of  a  point  is  not  a  point,  but  a  disk  whose  di- 
ameter depends  upon  the  size  of  the  aperture,  being  smaller 
for  large  ones  than  for  small.  If  you  are  looking  at  two 
distant  objects  (e.g.  a  double  star)  through  a  telescope, 
each  point  will  appear  as  a  disk,  and  the  smaller  are  the 
disks  the  less  will  they  tend  to  overlap  and  produce  a 
blurred  effect.  Hence,  if  great  resolving  power  is  required, 
the  disks  must  be  as  small  as  possible,  and  this  demands  a 
large  aperture.  The  first  great  reflector  (that  of  Lord  Rosse) 
was  made  more  than  half  a  century  ago,  and  was  6  feet  in 
diameter.  After  a  time  a  reaction  set  in  against  reflectors, 
but  they  have  come  into  prominence  again  of  late,  and  now 
such  an  instrument,  with  the  enormous  aperture  of  100 
inches,  is  being  made  for  the  Mt.  Wilson  Solar  Observatory. 
As  to  focal  length,  the  advantage  of  increasing  this  is  that 
the  size  of  the  image  is  magnified  in  proportion.  If  you 
double  AS,  you  double  the  image,  but  there  is  a  correspond- 
ing disadvantage  in  greater  length  of  telescope,  and  so 
greater  inconvenience  and  expense.  Lord  Rosse's  telescope 
had  a  focal  length  of  54  feet  and  was  exceedingly  cumbrous. 
Having  considered  such  questions  as  the  size,  form,  and 
material  of  the  reflector,  you  may  look  for  a  moment  at 
the  problem  of  making  the  glass  support  for  the  reflecting 
film  of  silver.  The  glass  must  be  as  free  as  possible  from 
flaws  or  strains,  so  as  to  minimize  the  danger  of  a  change 
of  shape,  and  to  obtain  a  suitable  disk  of  glass  proves,  in 
the  case  of  a  very  large  reflector,  a  very  arduous  process. 
Once  this  has  been  secured,  the  front  surface  of  the  disk  is 
made  concave  by  means  of  a  tool  of  suitable  curvature.  It 
is  important  to  avoid  differences  of  curvature  in  different 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        147 

parts  of  the  surface,  and  any  errors  of  this  kind  can  be 
detected  with  extraordinary  nicety  —  merely  placing  the 
finger  on  the  glass  will  cause  a  swelling  of  the  surface  that 
can  easily  be  detected.  After  a  uniform  curvature  has 
been  obtained,  the  next  step  is  to  set  to  work  in  the  process 
of  polishing  to  hollow  out  the  surface  in  the  center  so  as  to 
produce  an  exact  paraboloidal  form,  any  departure  from  this 
form  being  readily  discovered  by  a  simple  optical  device. 


FIG.  38 

Then  the  surface  is  silvered  by  one  of  those  exceedingly 
ingenious  devices  of  modern  times  designed  for  this  end, 
and,  let  us  hope,  an  almost  perfect  reflector  is  the  result. 
Now,  if  such  an  instrument  were  turned  toward  a  star  or 
other  heavenly  body,  it  would  produce  an  image  of  the 
object  in  the  neighborhood  of  the  focus  S.  With  great 
focal  length  this  image  might  be  fifty  feet  or  more 
away  from  A,  and  so  would  be  inconveniently  placed  for 
purposes  of  close  inspection.  This  inconvenience  may 
be  avoided  by  intercepting  the  rays  as  they  converge 
toward  S,  and  reflecting  them  backward  so  as  to  converge 
to  a  point  C  behind  the  large  reflector  (Fig.  38).  It  is  a 
simple  problem  of  geometry  to  determine,  by  the  aid  of 
the  laws  of  reflection,  the  form  of  the  reflecting  surface 
that  will  produce  this  result.  The  surface  must  be  a  hy- 


148  LIGHT 

perboloid  formed  by  the  revolution  about  its  transverse 
axis  of  a  hyperbola  whose  foci  are  S  and  (7,  and  it  is  made 
by  the  same  general  processes  as  are  employed  in  forming 
the  paraboloid.  In  order  that  the  rays  should  reach  C. 
a  hole  would  have  to  be  made  in  the  center  of  the  large 
reflector  in  the  neighborhood  of  A.  This  has  been 
done  in  some  telescopes,  but  the  plan  has  many  disadvan- 
tages, and  these  may  be  avoided  by  again  intercepting 
the  rays  as  they  converge  toward  C  by  a  small  plane  mirror 
at  D,  and  reflecting  them  to  one  side  so  as  to  form  an  image 
at  F.  A  reflecting  apparatus  made  in  this  way  will  give 
very  good  definition  near  the  optic  axis,  but  if  the  rays  are 
oblique  to  this  axis  the  images  will  be  indistinct.  It  is 
therefore  important  that  the  instrument  should  be  kept  in 
almost  perfect  adjustment,  and  the  greatest  care  must  be 
employed  to  secure  this,  if  the  best  results  are  to  be  obtained. 
Thus  far,  in  considering  the  formation  of  an  image  of  an 
object*  we  have  supposed  that  this  is  achieved  by  means  of 
reflection.  You  need  scarcely  be  reminded  that  the  same 
end  can  be  reached  by  means  of  refraction.  You  must 
all  be  more  or  less  familiar  with  the  action  of  a  lens  in 
bringing  the  rays  of  light  from  a  point  to  a  focus,  and  it  is 
not  difficult  to  investigate  the  features  of  the  image  thus 
formed,  by  aid  of  the  laws  of  refraction.  What  has  already 
been  said  as  to  the  size  of  the  aperture  and  the  focal  length 
of  the  lens  applies  to  a  refractor  just  as  to  a  reflector. 
The  form  of  the  refracting  surfaces  is  determined  mainly 
from  the  consideration  that  two  defects  must  be  specially 
guarded  against,  these  being  known  technically  as  chro- 
matic effects  and  spherical  aberration.  The  latter  defect 
has  already  been  referred  to,  without  the  name.  It  has  been 
remarked  that  if  rays  from  a  point  strike  a  surface  obliquely, 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        149 


they  are  not  brought  (either  by  reflection  or  refraction) 
to  the  same  focus  as  when  they  strike  the  surface  almost 
at  right  angles.  If,  then,  we  have  a  number  of  rays  striking 
such  a  surface,  some  of  them  nearly  normally  and  others 
much  more  obliquely,  there  will  be  no  definite  image  of  a 
point,  and  the  whole  image  will  be  blurred  and  indistinct. 


FIG.  39 

Investigation  shows  that  it  is  possible  to  lessen  this  indis- 
tinctness by  increasing  the  number  of  refracting  surfaces. 
A  common  arrangement  is  to  have  a  double  objective,  such 
as  is  illustrated  in  Fig.  39  a.  This  is  made  of  two  lenses 
of  glass  of  different  refractive  powers,  one  (Lj)  of  flint  and 
the  other  (L2)  of  crown  glass.  The  curvatures  of  the  various 
surfaces  are  arranged  so  as  to  make  the  defect  due  to  rays 
striking  one  surface  obliquely  counterbalance  that  due  to 
the  other  surfaces,  and  in  every  objective  of  any  value 
this  is  done  with  great  precision. 


150  LIGHT 

In  constructing  the  lenses  it  is  important  to  avoid  hav- 
ing different  curvatures  in  different  belts  of  the  lenses,  as 
this  will  inevitably  introduce  aberration  and  cause  a  blur. 
Also,  as  the  curvature  of  each  surface  must  be  maintained 
constant,  care  must  be  taken  to  avoid  its  change  due  to 
fluctuations  of  temperature,  to  flexure  from  the  weight, 
or  any  other  causes.  The  danger  of  flexure  is  of  course 
much  less  serious  with  small  lenses  than  with  the  large  ones 
such  as  those  of  the  great  40-inch  refractor  of  the  Yerkes 
Observatory.  To  avoid  flexure  with  such  large  lenses,  we 
must  have  considerable  thickness  in  the  center  of  the  lens, 
and  this  introduces  a  serious  defect  when  the  telescope  is 
to  be  used  for  photographic  purposes.  The  amount  of 
light  absorbed  in  passing  through  a  considerable  thickness, 
even  of  the  clearest  glass,  is  far  from  negligible,  and  it  in- 
creases enormously  for  those  light-waves  of  high  frequency 
which  play  the  leading  part  in  photographic  work.  Hence, 
if  we  wish  to  take  a  photograph  of  a  faint  object,  so  that 
we  cannot  afford  to  lose  much  light,  a  thick  lens  is  objec- 
tionable. This  is  one  of  the  reasons  why  refractors  are 
being  replaced  by  reflectors  for  some  of  the  work  in  modern 
astronomy.  Perhaps  a  stronger  reason,  however,  is  that 
the  reflector  avoids  entirely  the  serious  difficulties  due  to 
chromatic  or  color  effects.  The  law  of  reflection  is  the 
same  for  all  colors,  so  that  the  position  of  the  image  after 
any  number  of  reflections  is  quite  independent  of  the 
color  of  the  light,  and  no  chromatic  effects  can  possibly  be 
introduced  by  the  process  of  reflection.  With  refraction, 
however,  it  is  very  different.  The  laws  of  refraction  show 
that  the  position  of  the  image  depends  on  the  refractive 
index  of  the  refractor,  and  this  again  depends  on  the  color 
of  the  incident  light.  White  light,  as  we  have  seen,  is  a 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        151 

composite  of  many  colors,  and  the  image  formed  by  each 
of  its  constituents  will  be  in  a  different  place,  and  of  a 
different  size.  Clearness  and  precision  in  the  image  thus 
appear  to  be  impossible,  and  the  question  must  arise  —  can 
this  be  avoided  ?  The  answer  is  that  it  can,  at  least  in  a 
partial  manner.  If  we  have  two  lenses,  one  may  be  made 
of  such  a  form  and  material  that  it  will  throw  the  red  image 
farther  away  than  the  blue,  while  the  other  reverses  things 
by  throwing  the  blue  farther  away  than  the  red.  In  com- 
bination it  may  be  arranged  that  they  throw  the  two  images 
together.  This  is  one  reason  why  the  objective  of  an 
astronomical  telescope  is  always  made  up  of  at  least  two 
lenses,  such  as  the  double  objective  depicted  in  Fig.  39  a. 
It  is  an  easy  matter  to  calculate  how  to  arrange  two  lenses 
of  given  materials  so  as  to  combine  any  two  given  colors. 
If  the  telescope  is  to  be  used  for  visual  work,  it  is  natural 
to  combine  two  colors  to  which  the  eye  is  most  sensitive, 
such  as  green  and  yellow.  This  combination,  however, 
will  be  of  little  use  for  photographic  work,  as  the  rays  that 
are  most  important  in  that  field  have  been  neglected.  To 
improve  matters,  we  may  do  as  Ritchey  did  with  the  Yerkes 
refractor,  and  put  in  a  yellow  screen  to  cut  out  the  blue 
and  violet;  but  of  course  we  do  this  at  the  expense  of  the 
light  that  is  most  effective  photographically,  and  it  is  often 
our  great  end  to  conserve  what  little  light  there  is.  In  any 
case,  when  two  differently  colored  images  have  been  com- 
bined in  this  way,  the  other  colored  images  are  not,  as  a 
rule,  combined.  Their  presence  in  different  positions  gives 
rise  to  what  are  called  secondary  spectra,  which  not  only 
produce  indistinctness,  but  cause  a  considerable  loss  in  the 
light  that  contributes  effectively  to  the  brightness  of  the 
image.  Thus  it  has  been  calculated  that  the  loss  from 


152  LIGHT 

this  cause  with  the  Lick  36-inch  refractor  was  about  one- 
quarter  of  the  whole  light,  and  with  other  refractors  of 
shorter  focal  length  the  loss  was  considerably  greater. 
Modern  researches  and  experiments  in  the  manufacture 
of  glass  have  made  it  possible  to  select  two  glasses  that 
in  combination  avoid  these  secondary  spectra  almost 
entirely.  Unfortunately,  however,  the  objectives  so  made 
have  not  been  wholly  free  from  defects,  the  most  important 
arising  from  a  lack  of  permanence  in  the  quality  of  the 
glass.  With  a  triple  objective  consisting  of  three  lenses, 
Z/1;  L2,  Z/g,  such  as  is  depicted  in  Fig.  39  b,  the  chro- 
matic effects  can  be  avoided  almost  perfectly,  but  as  yet 
no  very  large  refractors  have  been  equipped  in  this  fashion. 
The  cost,  of  course,  is  greater,  and  the  extra  lens  in- 
volves more  loss  of  light  by  absorption,  a  serious  thing, 
as  we  have  seen,  especially  in  the  photography  of  faint 
objects. 

So  far  we  have  been  occupied  entirely  with  the  design 
and  construction  of  the  objective,  which  forms  the  image 
of  an  object,  whether  by  reflection  or  refraction.  We  have 
still  to  inquire  what  means  are  employed  to  get  a  close  view 
of  the  image  so  formed.  For  this  purpose  an  eye-piece  is 
used,  and  this  is  designed  to  magnify  the  image,  just  as 
when  you  take  up  a  hand  magnifier  to  look  closely  at  a 
small  object.  Our  time  is  too  far  exhausted  to  enable  us 
to  go  into  details  as  to  the  arrangement  of  the  parts  of  this 
eye-piece.  Suffice  it  to  say  that,  as  a  rule,  it  consists 
of  two  lenses  so  constructed  and  placed  as  to  diminish  as 
much  as  possible  the  defects  due  to  spherical  aberration 
and  the  chromatic  effects.  It  is  not  completely  achromatic, 
but  an  effort  is  made  to  bring  it  about  that  the  different 
colored  images  that  are  formed  should  have  the  same 


THE  LAWS  OF  REFLECTION  AND  REFRACTION        153 

apparent  size,  as  this  avoids  the  indistinctness  due  to  a 
series  of  colored  images  overlapping  one  another. 

The  point  that  I  have  hoped  to  make  clear  to  you  in  the 
latter  part  of  this  lecture  is  that  the  design  and  construction 
of  a  modern  optical  instrument  is  no  haphazard  process, 
guided  by  rule  of  thumb.  On  the  contrary,  every  detail  is 
carefully  planned  and  calculated  with  the  aid  of  the  funda- 
mental laws  of  reflection  and  refraction.  Calculation,  on 
the  basis  of  these  principles,  determines  the  size  and  the 
form  of  the  various  parts;  calculation  determines  their 
relative  position,  calculation  determines  even  the  ma- 
terials of  which  they  are  made.  Absolutely  nothing  is 
left  to  chance  or  guesswork;  everywhere  law  and  intelli- 
gence are  supreme. 


VII 

THE  PRINCIPLE  OF  INTERFERENCE 

THUS  far,  in  dealing  with  the  theory  of  light,  we  have 
emphasized  the  idea  of  a  periodic  disturbance  propagated 
through  a  medium,  and  we  have  emphasized  this  because 
the  idea  of  periodicity  is  the  fundamental  one.  Any  such 
periodic  disturbance  may  be  called  a  wave,  and  the  theory 
a  wave  theory  of  light;  but  it  will  be  well  to  guard  your- 
selves against  being  misled  by  following  too  closely  the 
analogy  presented  by  the  familiar  phenomena  of  water 
waves.  Here,  too,  you  have  the  fundamental  idea  of  a 
periodic  disturbance  propagated  with  a  definite  velocity, 
and  it  is  doubtless  because  of  this  that  the  phrase  a  wave 
of  light  is  so  generally  employed.  The  analogy,  however, 
is  not  complete,  and  must  not  be  pressed  too  hard;  for 
one  reason,  water  waves,  as  ordinarily  observed,  are  sur- 
face phenomena;  if  you  could  see  what  goes  on  below  the 
surface,  the  analogy  would  be  much  more  instructive.  At 
the  same  time  there  is  much  that  arises  in  discussing  light 
that  can  be  most  conveniently  spoken  of  in  language  that 
is  suggested  by  the  familiar  phenomena  of  water  waves. 
A  common  term  when  dealing  with  such  matters  is  the 
wave-length.  In  the  case  of  waves  in  water  this  is  some- 
thing that  you  can  readily  see  and  measure,  the  distance 
from  crest  to  crest  of  consecutive  waves.  Suppose  that  you 
are  watching  a  swarm  of  corks  floating  on  the  water,  and  ob- 
serve how  they  rise  and  fall  as  waves  pass  over  them.  If 

154 


THE  PRINCIPLE  OF  INTERFERENCE  155 

you  fixed  your  attention  on  two  successive  corks,  each  of 
which  was  at  the  highest  point  of  its  path,  they  would,  of 
course,  be  each  on  the  crest  of  successive  waves.  After  a 
definite  interval  of  time  (the  period)  they  would  each 
once  more  be  on  the  crest  of  a  wave,  having  fallen  and 
risen  in  the  interval  as  the  wave-form  advanced.  The 
wave-length  is  the  distance  from  crest  to  crest,  and  you 
can  see  that  there  must  be  a  relation  between  the  wave- 
length (X),  the  velocity  of  the  wave-form  (v),  and  the  period 
(p  =  l//;  where /is  the  frequency).  This  relation  is,  in  fact, 
\  =  vp  =  v/f.  In  the  case  of  light  the  velocity  is  always  the 
same  where  there  is  no  matter  (that  it  changes  with  the 
frequency  in  the  presence  of  matter  was  explained  at  con- 
siderable length  in  the  lecture  on  Dispersion).  Hence,  as 
the  frequency  (/)  changes  with  the  color  of  the  light,  so 
must  the  wave-length  (X).  In  other  words,  differently 
colored  waves  have  different  lengths.  Waves  of  high  fre- 
quency, such  as  violet  waves,  are  short;  waves  of  lower 
frequency,  such  as  red  waves,  are  longer ;  what  the  actual 
lengths  are  and  how  they  are  measured  will  appear  in  a 
later  lecture. 

So  far  we  have  spoken  of  a  single  train  of  waves ;  but 
what  if  more  than  one  train  moves  across  the  same  space  ? 
It  is  an  interesting  and  instructive  thing  to  observe,  if  a 
sheet  of  water  be  at  hand.  Throw  in  two  stones  at  A  and  B 
respectively.  You  will  see  a  wave-form  running  outward 
from  each  of  these  centers,  and  in  due  time  the  two  trains  of 
waves  will  cross  one  another's  path.  A  curious  pattern  will 
be  the  result,  and  you  may  learn  much  by  trying  to  account 
for  its  leading  features.  The  clue  to  everything  here  is 
the  Principle  of  Superposition  of  Small  Motions,  or  the 
Principle  of  Interference  as  it  is  usually  called  when  its 


156  LIGHT 

applications  to  optical  phenomena  are  under  considera- 
tion. The  principle  lays  down  a  rule  for  determining  the 
effect  of  combining  two  small  displacements  due  to  dif- 
ferent causes.  It  states  that  each  cause  produces  the 
same  effect  as  it  would  were  the  other  cause  absent,  and 
that  in  computing  the  displacement  due  to  the  combina- 
tion of  both  causes  we  have  merely  to  add  together  the 
displacements  due  to  each  separately,  of  course  taking 
account  of  the  direction  of  the  displacements  in  the  process 
of  addition.  Thus,  if  the  motion  due  to  one  cause  would 
raise  a  point  an  inch,  and  that  due  to  another  would  raise 
it  half  an  inch,  then  the  point  would  be  raised  1  +  J,  or 
an  inch  and  a  half,  under  the  combined  influence  of  both 
causes.  If,  on  the  other  hand,  one  cause  would  raise  a 
point  an  inch  and  the  second  depress  it  half  an  inch,  the 
combination  would  raise  it  1  —  J,  or  half  an  inch.  Sup- 
pose that  we  accept  this  principle  and  apply  it  to  two 
trains  of  water  waves  of  the  same  height  and  length,  and 
moving  in  the  same  direction.  What  would  be  the  com- 
bined effect  of  two  such  waves?  The  answer  would  de- 
pend entirely  on  their  relative  phase.  If  crest  corresponded 
to  crest  so  that  the  waves  were  "in  phase,"  the  two  would 
combine  into  a  single  wave  of  double  the  height  of  each. 
If,  however,  crest  corresponded  to  furrow,  so  that  there 
was  a  difference  of  phase  of  half  a  wave-length,  then  the  com- 
bination would  produce  no  wave  at  all,  but  absolute  rest. 
The  crest  of  one  would  just  fill  up  the  furrow  of  the  other, 
and  the  two  waves  might  be  said  to  interfere  with  one  an- 
other. It  is  on  this  account  that  the  principle  is  com- 
monly spoken  of  as  Interference.  It  is  a  principle  that 
was  well  known  to  Newton,  and  was  applied  by  him  to 
explain  certain  phenomena  of  the  tides.  However,  it  was 


THE  PRINCIPLE  OF  INTERFERENCE  157 

reserved  for  another  great  Englishman,  Thomas  Young, 
to  realize  that  the  same  principle  is  applicable  to  light  and 
to  use  it  as  a  means  of  overcoming  most  of  the  obstacles 
that  had  retarded  the  progress  of  the  science  of  optics. 
Young's  is  one  of  the  very  greatest  names  in  science, 
although  almost  wholly  unknown  to  the  man  in  the  street. 
He  was  endowed,  according  to  Helmholtz,  with  "one  of 
the  most  profound  minds  that  the  world  has  ever  seen." 
His  application  of  the  Principle  of  Interference  to  light 
was  only  one  of  his  strokes  of  genius ;  but  it  was  far-reach- 
ing in  its  consequences,  and  made  Young  in  a  sense  the 
father  of  the  wave  theory  of  light.  It  was  he,  more  than 
any  one  else,  who,  in  the  early  days,  just  a  century  ago, 
turned  men's  speculations  along  the  track  that  has  led  to 
so  much  in  more  recent  times.  Perhaps  you  would  like 
to  hear  how  he  expressed  himself,  as  it  is  always  interest- 
ing to  listen  to  an  original  thinker  when  he  is  expounding 
his  own  ideas.  Here,  then,  is  a  brief  extract  from  his 
writings  on  the  subject  of  Interference:  — 

"It  was  in  May,  1801,  that  I  discovered,  by  reflecting 
on  the  beautiful  experiments  of  Newton,  a  law  which  ap- 
pears to  me  to  account  for  a  greater  variety  of  interesting 
phenomena  than  any  other  optical  principle  that  has  yet 
been  made  known.  I  shall  endeavor  to  explain  this  law 
by  a  comparison.  Suppose  a  number  of  equal  waves  of 
water  .to  move  upon  the  surface  of  a  stagnant  lake  with 
a  certain  constant  velocity,  and  to  enter  a  narrow  channel 
leading  out  of  the  lake.  Suppose,  then,  another  similar 
cause  to  have  excited  another  equal  series  of  waves,  which 
arrive  at  the  same  channel  with  the  same  velocity  and  at 
the  same  time  with  the  first.  Neither  series  of  waves 
will  destroy  the  other,  but  their  effects  will  be  combined; 


158  LIGHT 

if  they  enter  the  channel  in  such  a  manner  that  the  eleva- 
tions of  one  series  coincide  with  those  of  the  other,  they 
must  together  produce  a  series  of  greater  joint  elevations; 
but  if  the  elevations  of  one  series  are  so  situated  as  to 
correspond  to  the  depressions  of  the  other,  they  must 
exactly  fill  up  those  depressions,  and  the  surface  of  the 
water  must  remain  smooth;  at  least  I  can  discover  no 
alternative,  either  from  theory  or  from  experiment.  Now 
I  maintain  that  similar  effects  take  place  whenever  two 
portions  of  light  are  thus  mixed,  and  this  I  call  the  general 
law  of  the  Interference  of  Light.  I  have  shown  that  this 
law  agrees  most  accurately  with  the  measures  recorded  in 
Newton's  "  Opticks,  "  relative  to  the  color  of  transparent 
substances,  observed  under  circumstances  which  had  never 
before  been  subject  to  calculation,  and  with  a  great  di- 
versity of  other  experiments  never  before  explained." 

I  shall  direct  your  attention  in  a  moment  to  some  ex- 
periments designed  to  test  or  illustrate  the  Principle  of 
Interference,  but  before  doing  this  I  should  perhaps  state 
explicitly  that  in  applying  it  to  the  explanation  of  optical 
phenomena  you  are  not  restricting  yourself  to  any  special 
form  of  the  wave  theory  of  light.  It  is  a  principle  that  is 
applicable  to  displacements  of  any  kind,  and  its  most  im- 
portant consequence  for  our  present  purposes  is  that  an 
upward  displacement  in  the  ether  due  to  one  cause  may 
be  exactly  counteracted  by  an  equal  and  opposite  down- 
ward movement  due  to  some  other  cause,  and  that  this 
will  inevitably  be  the  case  if  there  be  a  certain  phase  rela- 
tion between  the  two  periodic  movements.  It  is  in  this 
way  that  two  lights  may  produce  darkness  in  certain 
places,  although  it  may  at  first  seem  paradoxical  that  a 
combination  of  lights  should  produce  darkness.  Further- 


THE  PRINCIPLE  OF  INTERFERENCE 


159 


more,  if  you  are  to  understand  the  experiments  that  are 
about  to  be  referred  to,  you  should  call  to  mind  that  white 
light  is  of  a  composite  character,  and  that,  by  suppressing 
some  of  its  constituents,  color  effects  are  produced.  At 
one  place  blue  may  be  suppressed  by  interference,  at  an- 
other green,  and  at  another  red,  so  that  interference  phe- 
nomena should  be  characterized  by  bands  of  color  wher- 
ever white  light  is  employed  in  producing  them. 


E 


FIG.  40 


One  of  the  most  famous  of  Young's  experiments  to 
test  his  theory  of  interference  is,  in  principle,  as  fol- 
lows. Light  is  allowed  to  stream  through,  say,  a  verti- 
cal slit  the  position  of  which  is  indicated  by  S  (Fig.  40), 
and  to  fall  on  two  other  vertical  slits,  A  and  B,  which 
are  very  close  to  one  another  in  a  screen  parallel  to  that 
containing  the  first  slit  S.  The  light  is  intercepted  on 
a  vertical  screen  indicated  by  the  section  ECPF  in  the 
figure.  Now  if  we  consider  a  point  such  as  P  on  this 
screen,  it  will  be  observed  that  it  is  illuminated  by  light 
that  comes  from  two  sources,  A  and  B  respectively.  As 
things  are  arranged,  the  light  that  sets  out  from  A  at  any 
moment  will  be  in  the  same  phase  as  that  which  has  B 
as  its  starting-point;  but  that  which  travels  to  P  along 
AP  will  reach  P  in  a  different  phase  than  the  light  from  B, 
for  the  two  started  together  and  moved  at  the  same  rate 
along  roads  of  different  lengths.  If  the  point  P  be  so 


160  LIGHT 

situated  that  the  difference  between  AP  and  BP  be  half 
a  wave-length,  or  any  odd  multiple  thereof,  the  two  lights 
reaching  P  will  interfere  and  nullify  one  another.  Hence 
the  screen  EF  will  not  be  uniformly  illuminated,  but  there 
will  be  a  series  of  dark  vertical  lines,  or  of  colored  bands, 
according  as  the  incident  light  is  homogeneous  or  other- 
wise. If  one  of  the  slits  (A  or  B)  be  covered,  the  bands 

should  disappear.  All  these 
phenomena  may  be  observed, 
and  the  position  of  the  bands 
and  the  arrangement  of  the 
colors  are  found  to  conform 
in  the  closest  manner  to  the 
predictions  of  the  theory  thus 
sketched.  Figure  41  gives  an 

indication  of  the  alternations  of  light  and  shade  on  the 
screen  EF. 

Unfortunately,  I  am  not  able  to  show  you  Young's 
experiment,  owing  to  the  difficulty  of  exhibiting  the 
phenomena  to  a  large  audience,  but  you  will  find  it  easy 
to  make  the  experiment  for  yourselves.  One  method  of 
proceeding  is  to  rule  two  narrow  lines  very  close  to  one 
another  on  a  photographic  plate  that  has  been  developed, 
and  then  to  look  through  the  slits  so  formed  at  the  light 
that  shines  through  a  slit  in  front  of  a  bright  light,  such  as 
the  electric  light.  A  still  simpler  procedure  is  to  make 
two  pinholes  close  to  one  another  in  a  card,  and  look 
through  them  at  the  light  streaming  through  another  hole. 
With  a  little  care  you  will  see  the  interference  fringes 
quite  distinctly.  Another  simple  experiment  designed  to 
show  interference  is  due  to  Fresnel,  one  of  the  great  names 
in  the  development  of  the  theory  of  light.  He  made  light 


THE  PRINCIPLE  OF  INTERFERENCE  161 

from  a  slit  S  (Fig.  42)  fall  on  two  mirrors,  A  and  B,  that 
had  their  edges  parallel  to  the  slit  and  their  planes  in- 
clined at  a  very  small  angle.  After  reflection  from  these 
two  mirrors,  the  two  streams  of  light  were  in  a  condition 
to  interfere  with  one  another,  and  a  series  of  bands  similar 
to  those  just  described  made  their  appearance  on  a  screen 
PE.  With  this  experiment,  as  with  Young's,  it  is  difficult 
to  arrange  things  so  as  to  exhibit  the  phenomena  to  many 


FIG.  42 

persons  at  once,  but  you  can  repeat  FresnePs  experiment  for 
yourselves.  Take  two  pieces  of  the  same  glass,  blacken 
them  on  the  back,  and  lay  them  on  a  board  that  is  covered 
with  a  black  cloth.  Raise  the  edge  of  one  strip  of  glass 
very  slightly,  and  adjust  the  slit  so  as  to  be  parallel  to  the 
common  edge  of  the  pieces  of  glass.  With  proper  care  in 
the  adjustment,  you  will  get  interference  fringes  exhibited 
to  the  eye  properly  placed  to  receive  the  light,  and  you 
will  find  that  these  fringes  disappear  if  one  of  the  reflected 
beams  is  suppressed  by  blackening  one  of  the  mirrors.  A 
modification  of  FresneFs  experiment,  due  to  Lloyd,  should 
perhaps  be  mentioned.  Take  a  strip  of  plate-glass  blackened 
at  the  back,  and  allow  light  to  fall  upon  it  at  nearly  grazing 
incidence,  as  in  Fig.  43.  Light  from  a  slit  S  reaches  a 
screen  at  P  by  two  paths,  one  directly  along  SP,  and  the 
other  along  SBP  after  reflection  at  the  mirror.  These  two 


162 


LIGHT 


beams,  the  one  direct  and  the  other  reflected,  may  inter- 
fere and  give  rise  to  fringes,  as  before.  In  this,  as  in  all 
the  experiments  referred  to  recently,  considerable  care 


must  be  exercised  in  the  adjustments,  otherwise  no  results 
or  spurious  results  will  be  obtained.  FresneFs  device,  and 
Lloyd's  modification  of  it,  consist  in  producing  interference 
between  the  two  parts  of  a  beam  that  have  been  separated 
by  reflection.  Fresnel  also  arranged  to  split  the  beam  by 
means  of  refraction.  To  do  this  he  employed  a  biprism, 
consisting  of  a  piece  of  glass  made  in  the  form  of  two 


FIG.  44 


prisms  of  very  small  angles  placed  back  to  back.  In  Fig.  44, 
the  shaded  portion  represents  a  biprism,  S  a  source  of  light, 
PE  a  screen.  The  light  from  S  that  falls  upon  the  upper 
portion  of  the  prism  is  bent  downwards  and  made  to  pro- 


THE  PRINCIPLE  OF  INTERFERENCE  163 

ceed  as  if  from  S^  while  that  which  falls  upon  the  lower 
portion  is  bent  upwards  and  proceeds  as  if  from  S2.  Thus 
Si  and  $2  correspond  to  A  and  B  in  Fig.  40,  representing 
Young's  experiment,  and  the  explanation  of  the  interfer- 
ence fringes  is  the  same  as  was  there  indicated. 

All  these  experiments  are  specially  designed  to  exhibit 
interference  fringes  and  to  test  the  explanation  by  a 
comparison  between  theory  and  observation  as  to  the 
exact  position  of  the  bands  and  the  arrangement  of  their 
colors.  Kindred  phenomena,  however,  are  obtained  in 
almost  countless  other  ways,  many  of  them  far  more 
striking  and  beautiful  than  those  to  which  reference  has 
just  been  made.  It  has  been  explained  that  in  order  that 
waves  of  light  may  interfere,  they  must  set  out  simul- 
taneously from  the  same  source  and  meet  with  such  dif- 
ferent treatment  that  one  wave  becomes  half  a  wave- 
length in  phase  behind  the  other.  Now  think  of  a  beam 
of  light  falling  on  a  thin  film  of  any  material.  Some  of 
the  light  will  be  reflected  at  the  first  face,  while  some  will 
penetrate  the  film,  be  reflected  at  the  second  face,  and, 
after  emerging  from  the  film,  be  in  a  condition  to  interfere 
with  what  was  first  reflected.  If  the  film  be  of  the  proper 
thickness,  this  interference  will  be  inevitable,  and  as  a 
consequence  some  of  the  light  will  be  suppressed  in  places, 
so  that  we  shall  see  alternations  of  light  and  darkness,  or 
variations  of  color,  according  as  the  incident  light  is 
homogeneous  or  composite.  You  must  all  have  observed 
the  brilliant  colors  produced  in  this  way  by  a  thin  film  of 
oil  on  the  surface  of  water.  You  may  see  the  same  thing 
here  by  looking  at  the  beautiful  color  on  the  wall,  pro- 
duced by  reflecting  light  from  the  surface  of  the  water  in 
this  hand  tray  after  a  drop  of  turpentine  has  been  allowed 


164  LIGHT 

to  fall  upon  the  water.  Much  more  beautiful  effects,  due 
to  similar  causes,  are  obtained  with  a  soap-film,  as  every- 
body knows  who  has  seen  a  soap-bubble.  Fortunately, 
youth  is  not  a  question  of  age,  and  the  blowing  of  such 
bubbles  has  afforded  interest  and  amusement  to  genera- 
tions of  young  people  between  seven  and  seventy.  Nor 
have  philosophers  been  ashamed  to  enter  into  the  game 
and  to  discuss  the  phenomena  in  their  grave  way.  If  it 
be  true  that  to  the  poet's  mind 

"  the  meanest  flower  that  blows  can  give 
thoughts  that  do  often  lie  too  deep  for  tears/' 

then  it  need  cause  no  surprise  that  so  common  a  thing  as 
a  soap-bubble  has  engaged  the  serious  attention  of  the 
greatest  men  of  science,  such  as  Boyle  and  Newton  of 
olden  times,  Stokes  and  Kelvin  of  our  own  day,  to  select 
only  a  typical  few.  All  the  gorgeous  phenomena  of  color 
exhibited  by  soap-bubbles  are  explicable  by  means  of  the 
principle  of  interference.  The  color  that  is  suppressed  by 
interference  varies  with  the  thickness  of  the  film,  its  re- 
fractive index,  and  the  angle  of  incidence  of  the  light  that 
falls  upon  it.  Theory  enables  us  to  calculate  all  the 
details  and  to  predict  what  will  happen  with  a  film  of 
given  thickness  when  the  wave-lengths  corresponding  to 
the  different  colors  have  been  determined.  How  these 
wave-lengths  may  be  measured  will  be  indicated  in  a  later 
lecture  on  Diffraction.  Meanwhile,  as  the  phenomena  of 
the  soap-bubble  are  somewhat  complicated  by  the  curva- 
ture of  the  surface,  it  may  be  well  to  show  you  similar 
color  effects  with  a  flat  film.  I  dip  this  ring  into  a  solu- 
tion of  soap,  fix  it  in  a  vertical  plane,  and  by  means  of  a 
lens  bring  the  light  reflected  from  the  film  to  a  focus  on 


THE  PRINCIPLE  OF  INTERFERENCE  165 

the  screen.  The  exact  interference  effects  depend  on  the 
thickness  of  the  film,  and  therefore  change  as  the  thick- 
ness alters  while  the  liquid  streams  down.  The  image  on 
the  screen  is  inverted  by  the  lens,  so  that  everything 
appears  upside  down.  The  upper  part  of  the  film  is  seen 
at  the  bottom  of  the  picture  on  the  screen,  and  you  will 
observe  that  the  liquid  seems  to  be  streaming  upwards. 
Notice  the  changing  color  as  the  liquid  thins  away  from 
the  top  of  the  film.  First  you  see  a  bright  green,  then  it 
changes  gradually  until  now  you  have  a  deep  red.  Now, 
again,  in  this  part  it  is  blue,  now  violet,  now  quite  black, 
and  now  the  film  has  broken,  having  become  too  thin  to 
bear  the  strain  of  its  weight. 

An  interesting  modification  of  this  experiment  is  to 
arrange  things  so  that  the  light  comes  from  a  narrow  slit, 
and  after  reflection,  as  before,  from  the  film,  passes  through 
a  prism  before  falling  on  the  screen.  If  light  were  re- 
flected from  a  single  surface  and  treated  in  this  way,  the 
prism  would  separate  the  different  colors  and  produce  the 
familiar  spectrum.  With  the  film,  however,  there  will  be 
places  where  the  light  is  cut  out  by  interference,  so  that, 
as  the  film  thins,  dark  bands  will  be  seen  to  travel  across 
the  spectrum.  You  can  see  them  distinctly  in  the  ex- 
periment that  Mr.  Farwell  is  now  conducting. 

You  observed  in  these  experiments  with  films  that  just 
before  the  film  broke  it  looked  quite  black  at  the  thinnest 
part.  This  is  a  curious  fact,  and  one  that  seemed  para- 
doxical for  a  time.  Newton  observed  the  same  thing  with 
an  ordinary  soap-bubble,  and  you  can  easily  repeat  the 
observation.  Blow  such  a  bubble,  and  cover  it  with  a 
glass  to  screen  it  from  air  currents,  and  so  prevent  its 
breaking  too  soon.  As  the  liquid  drains  downwards,  the 


166  LIGHT 

film  gets  thinner  at  the  top,  and  just  before  it  breaks  this 
part  looks  quite  black.  At  first  sight  this  seems  contrary  to 
what  might  be  expected.  As  this  portion  of  the  film  is 
extremely  thin,  it  takes  practically  no  time  for  light  to 
travel  across  it  and  back  to  the  upper  surface,  so  that 
you  might  expect  the  light  that  has  made  this  short  pass- 
age to  be  in  the  same  phase  as  the  light  that  was  reflected 
at  the  first  surface.  If  this  were  so,  the  two  waves  should 
reinforce  one  another  instead  of  interfering,  so  that  we 
should  have  brightness  instead  of  darkness.  However,  on 
examining  the  matter  by  the  aid  of  theory,  it  appears  that 
at  one  of  the  reflections,  but  not  at  the  other,  there  should 
be  a  change  of  phase  of  half  a  wave-length  in  the  very 
act  of  reflection,  and  this  completely  accounts  for  what  is 
observed. 

All  the  bands  of  color  produced  by  interference  that 
you  have  seen  to-night  have  been  arranged  in  straight 
lines,  but  it  is  easy  to  get  them  in  other  forms.  Here, 
for  example,  is  a  simple  modification  of  our  experiment 
with  the  flat  film.  With  these  acoustical  bellows  I  pro- 
duce a  slight  blast  and  direct  it  almost  tangentially  on  the 
surface  of  the  film.  This  sets  the  liquid  in  the  film  in 
motion,  and  arranges  it  in  regions  of  varying  thickness, 
producing,  as  you  see,  brilliant  curves  of  color.  In  one 
case  you  have  a  series  of  concentric  circles,  such  an  arrange- 
ment of  color  as  is  found  in  the  famous  phenomena  of 
Newton's  Rings.  These  Newton  studied  with  great  care, 
the  second  book  of  his  "Opticks"  being  almost  wholly 
devoted  to  a  discussion  of  their  features.  Newton's  ar- 
rangement for  producing  these  rings  is  extremely  ingen- 
ious, because  extremely  simple  and  extremely  effective. 
It  consists  in  pressing  together  two  pieces  of  glass,  one  or 


THE  PRINCIPLE  OF  INTERFERENCE  167 

both  of  them  being  slightly  curved  (Fig.  45  a).  When 
light  is  allowed  to  fall  on  this  and  to  be  reflected,  a  beauti- 
ful series  of  colored  rings  is  seen  arranged  in  concentric 
circles  round  a  central  spot.  At  all  points  such  as  P 
(Fig.  45  b)  on  a  horizontal  circle  of  which  0  is  the  center, 
the  thickness  of  the  air-space  between  the  two  pieces  of 
glass  is  the  same,  and  equal  to  PN.  Thus  waves  that 
pass  to  and  fro  in  this  region  have  to  traverse  an  air  film 
of  this  thickness  (PN).  If,  then,  PN  be  of  the  length 
necessary  to  produce  the  requisite  phase  difference  for 


(a) 

FIG.  45 

waves  of  a  given  length,  there  will  be  interference,  and 
the  corresponding  color  will  be  absent  from  this  region. 
Thus,  we  should  expect  to  see  a  series  of  colored  rings  if 
the  incident  light  be  composite  like  sunlight,  and  there  is 
no  great  difficulty  in  predicting  the  main  features  from 
theory  and  verifying  the  correctness  of  this  theory  by 
careful  observation  of  what  actually  takes  place.  The 
most  important  laws  were  discovered  by  Newton  by  in- 
duction from  his  experimental  results.  Thus,  he  found  the 
law  of  the  radii  of  the  rings,  viz.  that  at  a  given  angle  of 
incidence  the  radii  of  the  different  rings  are  proportional 
to  the  square  roots  of  the  numbers  1,  2,  3,  4...  (These 
different  rings  are  spoken  of  as  rings  of  different  orders.) 
He  found  also  in  what  way  the  radii  varied  with  the  angle 
of  incidence,  and  verified  his  law  with  wonderful  accuracy, 
considering  the  rough  instruments  of  measurement  at  his 


168 


LIGHT 


disposal.  The  following  table  compares  the  radii  of  a 
ring  of  a  given  order  for  different  angles  of  incidence  on 
the  glass,  and  shows  how  Newton's  law  and  Newton's 
experiments  agreed  with  one  another.  Moreover,  by 
means  of  a  prism  Newton  analyzed  the  light  before  it  fell 


INCIDENCE 

o° 

10° 

20° 

30° 

Radius  (law) 

1 

10077 

1032 

1075 

Radius  (experiment)     .     . 

1 

1.0077 

1.033 

1.075 

INCIDENCE 

40" 

50° 

60° 

70° 

Radius  (law)    .         ... 

1.142 

1.247 

1.415 

1.71 

Radius  (experiment)     .     . 

1.140 

1.250 

1.4 

1.69 

upon  his  ring  apparatus,  and  so  was  enabled  to  inves- 
tigate the  phenomena  when  employing  light  of  a  single 
color,  and  to  see  in  what  way  a  change  of  color  affected 
the  size  of  the  rings  and  their  distinctness.  "I  found/' 
he  says,  "the  circles  which  the  red  light  made  to  be  mani- 
festly bigger  than  those  which  were  made  by  blue  and 
violet.  And  it  was  very  pleasant  to  see  them  gradually 
swell  or  contract  according  as  the  color  of  the  light  was 
changed."  As  the  radii  of  the  rings  depend  on  the  color, 
the  larger  (red)  rings  of  one  order  will  tend  to  overlap 
the  smaller  (blue)  rings  of  the  next  higher  order.  This 
overlapping  will  produce  indistinctness,  so  that  it  will  be 
difficult  to  see  the  rings  of  high  order  when  the  incident 
light  is  white.  If,  however,  homogeneous  light  be  em- 
ployed, there  is  no  possibility  of  overlapping,  so  that  far- 
more  rings  may  be  seen.  "I  have  sometimes,"  says  New- 
ton, "seen  more  than  twenty  of  them"  (when  working 


THE  PRINCIPLE  OF  INTERFERENCE  169 

with  a  prism  to  produce  homogeneous  light),  "whereas,  in 
the  open  air"  (without  the  prism),  "I  could  not  discern 
above  eight  or  nine."  Instead  of  using  a  prism,  we  may 
get  what  is  very  nearly  homogeneous  light  by  interposing 
colored  screens  in  front  of  the  powerful  electric  light  in 
the  lantern.  These  screens  cut  off  a  good  deal  of  the  light, 
so  that  the  phenomena,  as  you  see,  are  not  so  brilliant  as 
before;  but  if  you  look  carefully,  you  will  have  no  diffi- 
culty in  making  out  the  main  features.  Now  there  is  a 
red  screen  and  you  see  the  red  rings  (of  course  no  other 
color  is  possible  with  this  arrangement) ;  now  we  have  a 
blue  screen,  and  you  notice  the  blue  rings  distinctly  smaller 
than  the  red  ones  that  you  have  just  been  looking  at. 
Since  Newton's  day  there  have  been  many  modifications 
of  his  experiments  and  many  new  phenomena  of  a  kindred 
character  discovered;  but  there  is  nothing  that  is  not 
completely  accounted  for,  down  to  the  minutest  detail,  by 
means  of  the  principle  of  interference  coupled  with  the 
known  laws  of  reflection  and  refraction. 

All  these  examples  of  interference  have  been  produced 
by  apparatus  that  has  been  specially  designed  to  exhibit 
this  effect.  Not  infrequently,  however,  we  meet  with 
similar  phenomena  where  no  such  pains  has  been  taken 
to  produce  the  result.  In  such  cases  the  design,  if  design 
there  be,  is  not  of  man's  contrivance.  Thus  you  have  all 
observed  that  polished  steel  becomes  colored  when  it  is 
exposed  to  the  air.  A  thin  film  of  oxide  is  formed  on  the 
surface,  and  produces  interference  effects  by  reflection  like 
any  other  film.  Antique  glass,  especially  when  it  has  long 
been  buried,  becomes  coated  with  a  thin  layer  that  shows 
beautiful  interference  colors.  The  wings  of  a  butterfly 
owe  their  color  to  their  delicate  ribbed  structure  and  the 


170  LIGHT 

interference  that  this  produces.  The  gorgeousness  of  a 
peacock's  tail  is  due  to  the  same  cause.  You  will  observe 
that  the  color  of  this  feather  is  not  intrinsic ;  it  changes 
with  the  incidence  of  the  light,  as  you  see  when  I  turn  it 
in  the  lime-light.  The  changing  colors  of  opals  are  ex- 
plained in  the  same  way,  and  so  are  those  of  mother-of- 
pearl.  If  you  examine  such  an  object  closely  with  a 
microscope,  you  will  find  that  it  is  made  up  of  layers,  and 
that  the  surface  cuts  across  these  layers,  and  so  presents  a 
series  of  minute  grooves.  The  lights  that  are  reflected 
from  opposite  edges  of  these  grooves  are  in  the  condition 
to  interfere,  and  you  can  easily  see  that  the  color  changes 
with  the  incidence  of  the  light  that  falls  upon  the  surface. 
None  of  this  beautiful  color  is  really  in  the  shell.  Brewster 
showed  this  conclusively  when  he  stamped  the  shell  on 
black  wax,  thereby  reproduced  the  grooves,  and  obtained 
the  same  colors  from  the  wax  as  from  the  original  shell. 

Before  bringing  this  lecture  to  a  close,  there  is  just  time 
to  refer,  all  too  briefly,  to  an  ingenious  application  of  the 
principles  of  interference  to  the  problem  of  color  pho- 
tography. This  was  first  made  in  1891  by  Lippmann, 
but  since  that  date  considerable  improvements  have  been 
effected  in  the  practical  application  of  Lippmann's  ideas. 
The  theory  of  the  process  is  not  without  its  difficulties, 
but  the  broad  lines  of  the  explanation,  as  suggested  by  its 
author,  are  easily  seen.  The  first  matter  that  must  be 
firmly  grasped  is  that  there  is  an  intimate  relation  between 
the  intensity  of  light  reflected  from  a  very  thin  film  and 
its  thickness.  If  the  thickness  be  altered,  so  will  the 
brightness  of  the  reflected  beam.  We  saw  a  short  time 
ago  that  for  a  film  so  thin  that  it  can  scarcely  be  said  to 
have  any  thickness,  there  is  no  light  reflected  at  all.  Start- 


THE  PRINCIPLE  OF  INTERFERENCE  171 

ing  with  this,  let  us  imagine  the  thickness  to  increase 
gradually,  and  consider  the  effect  on  the  intensity  of  the 
reflected  light.  For  simplicity  we  shall  suppose  that  the 
light  is  incident  normally  and  not  obliquely.  The  re- 
flected light  will  grow  in  intensity  until  the  thickness  of 
the  film  is  exactly  half  a  wave-length  of  the  light  that  is 
used.  (That  length  will  depend,  as  has  been  seen,  upon 
the  color  of  the  light  and  upon  the  refractive  index  of  the 
film.)  After  this  thickness  of  half  a  wave-length  has 
been  reached,  less  light  will  be  reflected,  and  this  diminu- 
tion will  continue  until  a  thickness  of  a  wave-length  has 
been  attained,  when  once  more  there  will  be  no  reflected 
light.  This  variation  of  intensity  is  all  accounted  for  by 
the  principle  of  interference.  We  are  thus  led  to  the 
important  conclusion  that  when  dealing  with  thin  films 
less  than  a  wave-length  in  thickness,  we  immensely  in- 
crease their  reflecting  power  if  we  make  their  thickness 
half  a  wave-length  of  the  light  that  we  wish  to  reflect. 
Let  us  suppose  that  XR  is  the  wave-length  of  red  light 
for  the  material  of  which  the  film  is  composed,  and  that 
we  make  a  film  of  thickness  £  XR,  and  observe  the  light 
that  it  reflects  from  a  landscape  or  a  picture.  It  will  be 
much  more  effective  in  reflecting  red  than  any  other  color, 
and  its  power  of  selective  reflection  will  be  greatly  im- 
proved if  we  back  it  by  several  parallel  films  of  the  same 
thickness.  With  such  an  arrangement  we  shall  practi- 
cally see  nothing  but  the  red  parts  of  the  picture.  With 
other  films  of  thickness  %  XG,  where  XG  is  the  wave-length 
for  green  light,  we  shall  similarly  pick  out  the  green  por- 
tions, and  with  films  of  thickness  £  Xv  (where  Xv  is  the 
wave-length  of  violet  light)  the  violet  portions  of  our 
picture.  If,  now,  we  have  any  means  of  combining  these 


172  LIGHT 

three  colored  reflections,  we  shall  have  a  faithful  repre- 
sentation of  the  original,  according  to  the  explanation  set 
forth  in  the  earlier  lecture  on  color  photography. 

The  practical  difficulty  in  carrying  out  such  a  process 
that  will  probably  first  present  itself  to  your  minds  will 
be  that  of  obtaining  films  of  the  right  thickness.  The 
actual  lengths  of  some  waves  of  light  will  be  set  forth  in 
the  lecture  on  Diffraction,  and  if  you  have  any  conception 
of  their  minuteness,  measured  by  any  ordinary  standard, 
you  will  realize  that  it  is  quite  hopeless  by  any  mechanical 
process  to  produce  a  film  whose  thickness  is  exactly  J  XR, 
or  any  of  the  other  quantities  that  have  been  specified. 
And  yet  such  films  can  be  manufactured  quite  accurately 
by  optical  means.  The  device  for  doing  this  is,  of  course, 
an  essential  feature  of  the  Lippmann  process;  but  the 
same  principle  was  employed  a  little  earlier  by  Wiener. 
It  is  another  simple  application  of  the  Principle  of  Inter- 
ference. Suppose  that  we  have  two  series  of  waves  mov- 
ing through  a  medium,  and  that  they  are  similar  in  every 
other  respect  except  that  they  are  moving  in  opposite  direc- 
tions. These  waves  will  be  in  a  condition  to  interfere 
with  one  another,  and  there  will  be  a  series  of  points  N1} 
N2,  NB...  at  each  of  which  the  upward  displacement  in 
one  wave  is  exactly  counteracted  by  the  downward  dis- 
placement in  the  other  wave  that  is  moving  in  the  opposite 
direction.  At  such  points,  which  are  called  nodes,  the 
displacement  due  to  the  two  waves  will  be  zero.  At  inter- 
mediate points,  Lv  L2,  Z/3...,  the  two  displacements  will  be 
in  the  same  direction,  and  will  reinforce  one  another,  and 
these  points,  where  there  is  a  maximum  of  displacement, 
are  called  loops.  Investigation  shows  that  the  positions 
of  these  nodes  and  loops  are  stationary,  that  they  do  not 


THE  PRINCIPLE  OF  INTERFERENCE  173 

change  from  moment  to  moment.  The  aspect  of  this 
combination  of  two  trains  of  waves  is  thus  very  different 
from  that  of  either  taken  separately.  The  nodes  always 
remain  at  rest,  and  halfway  between  these  points  (at  the 
loops)  the  crests  of  the  waves  rise  and  fall  periodically. 
There  is  no  moving  of  the  wave-form  in  one  direction 
or  the  other,  but  a  mere  gradual  change  of  height.  Such 
a  set  of  waves  are  consequently  called  stationary  waves. 
They  have  often  been  set  up  in  air  and  water;  but  the 
difficulties  of  producing  them  with  light-waves  in  the 
ether  and  of  demonstrating  their  existence  were  not  suc- 
cessfully overcome  till  1890.  In  that  year  Wiener  set  up 
these  stationary  waves  by  reflecting  light  from  the  silver 
coating  of  a  plate  of  glass,  and  proved  their  existence  by 
their  effect  on  a  thin  film  of  sensitized  collodion  super- 
posed on  the  glass.  We  should  expect  the  photographic 
action  to  be  different  at  the  nodes,  where  there  is  no  dis- 
placement, than  at  the  loops  where  the  displacement  is 
greatest,  and  Wiener  succeeded  in  showing  that  the  pho- 
tograph was  crossed  by  bright  and  dark  bands  at  regular 
intervals,  and  thus  in  affording  another  ocular  demon- 
stration of  the  soundness  of  the  Principle  of  Interference. 
Now  there  is  one  feature  of  these  stationary  waves  that 
has  not  yet  been  mentioned  and  that  is  specially  impor- 
tant for  the  purpose  that  we  have  in  hand.  The  distance 
between  successive  loops,  as  well  as  that  between  successive 
nodes,  is  exactly  half  a  wave-length.  You  will  realize  the 
significance  of  this  at  once.  It  gives  us  an  optical  means 
of  producing  a  film,  or  a  series  of  parallel  films,  whose 
thickness  is  half  a  wave-length  of  any  color  that  we  wish 
to  use.  Set  up  these  stationary  waves  with  red  light,  and 
they  will  so  act  on  the  sensitive  emulsion  as  to  arrange  it 


174  LIGHT 

effectively  in  layers  whose  thickness  is  £  XB,  and  when  this 
is  afterwards  viewed  by  reflection  it  will  send  back  practi- 
cally nothing  but  red  light.  Do  the  same  with  the  other 
colors,  and  this  part  of  your  problem  is  solved.  You  will 
probably  see,  too,  that  it  is  not  really  necessary  to  have 
these  different  films  and  to  devise  a  means  of  combining 
the  pictures  that  they  present  by  reflection.  All  the  work 
can  be  done  by  the  same  material.  Each  color  that 
strikes  it  will  build  up  a  little  film  by  means  of  stationary 
waves  acting  on  the  sensitive  emulsion  with  special  force 
at  regular  intervals  of  half  a  wave-length,  and  this  film  will 
be  of  just  the  right  thickness  to  reflect  that  particular 
color  most  copiously.  The  form  of  the  object  will  be 
produced,  just  as  in  ordinary  photography,  by  the  grada- 
tions of  light  and  shade  over  different  portions  of  the  plate, 
the  color  by  the  thickness  of  the  different  films  beneath 
the  several  portions. 


VIII 


CRYSTALS 

TO-NIGHT  we  are  to  deal  with  some  of  the  optical 
properties  of  crystals.  It  has  been  remarked  in  an  earlier 
lecture  that  the  distinguishing  feature  of  a  crystal  is  its 
structure.  Its  parts  are  not  thrown  together  at  random, 
but  are  built  one  upon  another  according  to  some  definite 
plan.  The  result  is  that  a  crystal  does  not  seem  the 
same  when  looked  at  from  different  directions.  If  you 
could  imagine  yourself  moving  through  water  or  glass 
(which  are  not  crystals),  it  would  make  no  difference  to 
your  rate  of  progress  whether  you  went  north,  south, 
east,  or  west.  In  a  crystal,  however,  it  might  well  be 
different;  the  structure  might  be  so  arranged  as  to  make 
progress  easier  in  one  direction  than  in  another.  In 
optical  problems  we  are  interested  especially  in  the  propa- 
gation of  waves,  the  speed  of  which  for  a  medium  like 
the  ether  depends  on  the  rigidity  of  that  medium.  Here 
we  need  not  stop  to  inquire  exactly  how  the  presence  of 
matter  modifies  the  effective  rigidity  of  the  ether  contain- 
ing it ;  but  owing  to  the  structure  of  a  crystal  it  is  natural 
to  suppose  that  its  presence  in  the  ether  will  modify  the 
rigidity  differently  in  different  directions.  If  we  apply 
general  dynamical  principles  to  the  discussion  of  the 
propagation  of  waves  in  such  a  medium  (that  is,  a  medium 
with  different  rigidities  in  different  directions),  the  first 

175 


176 


LIGHT 


striking  result  that  we  reach  is  that,  as  a  general  rule,  for 
a  wave  traveling  in  any  given  direction  there  are  two 
speeds  with  which  the  wave  can  travel.  We  may  express 
this  by  saying  that  two  waves  can  travel  through  a  crystal 
in  any  given  direction,  and  that  in  general  these  will 
travel  with  different  speeds.  As  there  is  a  ray  of  light 
corresponding  to  each  wave,  we  see  that  when  a  ray  strikes 
a  crystal  it  will  give  rise  not  to  one,  but  to  two  different 
rays  within  the  crystal.  This  prediction  from  theory  cor- 


(o) 


FIG.  46 


responds  to  the  well-known  fact  of  double  refraction  pro- 
duced by  a  crystal.  Here  are  two  double  prisms  of  the 
same  size  and  shape.  They  are  represented  in  section  in 
Fig.  46  a  and  b.  The  first  is  made  of  two  prisms,  ABD 
and  BDC,  of  the  same  non-crystalline  material,  glass. 
The  second  (Fig.  46  b)  is  made  in  exactly  the  same  way, 
but  is  of  crystal,  Iceland  spar.  Now  observe  the  difference 
of  behavior  when  a  ray  of  light  falls  perpendicularly  on  a 
face  of  each  double  prism  and  is  afterwards  received  on 
a  screen  behind  the  prism.  With  the  glass  the  ray  goes 
straight  through  as  indicated  in  Fig.  46  a  and  forms  a 
single  patch  at  P  on  the  screen.  With  the  crystal  the 
ray  splits  into  two  on  crossing  B'D',  each  of  these  rays  is 
further  bent  on  passing  out  of  the  prism,  and  on  the  screen 
we  see  two  widely  separated  spots  of  light,  one  at  Pl  and 


CRYSTALS  177 

the  other  at  P2-    You  see,  then,  that  this  double  refraction 
is  no  dream  of  the  theorists,  but  an  actual  fact. 

Theory,  however,  does  much  more  than  predict  that 
we  should  find  two  waves  traveling  in  a  given  direction 
with  different  speeds.  It  indicates,  further,  and  this  is 
very  important,  that  these  two  waves  will  be  differently 
polarized.  When  each  is  plane  polarized,  the  planes  of 
polarization  for  the  two  waves  are  at  right  angles  to  one 
another.  This  deduction  from  theory  is  amply  verified 
by  experiment,  and  the  use  of  crystals  to  produce  or  to 
test  plane  polarized  light  is  one  of  the  regular  resources 
of  an  optical  laboratory.  You  may  remember  that  in 
introducing  the  subject  of  Polarization  we  employed  a 
Nicol's  prism  to  produce  plane  polarized  light.  Its  power 
of  doing  this  depends  entirely  on  its  crystalline  structure, 
and  you  should  have  no  difficulty  in  understanding  its 
action  if  you  bear  in  mind  two  facts.  The  first  is  the  one 
just  referred  to,  that  for  a  given  ray  in  a  crystal  the  vibra- 
tions must  be  confined  to  one  or  other  of  two  planes  at 
right  angles,  say  a  vertical  and  a  horizontal  plane.  It 
appears  that  the  molecules  of  a  crystal  are  so  arranged 
that  the  ether  cannot  continue  to  vibrate  to  and  fro  along 
any  arbitrary  direction,  but  must  confine  its  movements 
to  one  or  other  of  two  directions  at  right  angles  to  one 
another.  A  mechanical  analogue  was  suggested  on  p.  101 
and  illustrated  in  Fig.  24 ;  but  it  may  not  be  out  of  place 
to  repeat  that  this  is  merely  an  analogy,  and  that  it  is 
not  suggested  that  the  figure  depicts  the  actual  arrange- 
ment of  the  molecules.  The  second  fact  to  remember  in 
dealing  with  Nicol's  prism  is  the  fact  of  total  reflection 
when  the  angle  of  incidence  exceeds  the  critical  angle. 
NicoFs  prism  is  made  by  cementing  together  two  prisms 


178  LIGHT 

of  Iceland  spar,  as  indicated  in  Fig.  47.  When  a  ray  AB 
strikes  the  prism,  it  is  split  into  two  by  double  refraction, 
and  the  two  rays  in  the  crystal  EG  and  BF  are  differently 
polarized,  BC  horizontally  (say)  and  BF  vertically.  The 
angles  of  the  prisms  are  so  arranged  that  BF  strikes  the 
thin  layer  of  cement  between  the  prisms  at  an  angle  greater 
than  the  critical  angle.  Thus,  the  ray  BF  is  totally  re- 
flected along  FH,  and  so  does  not  emerge  from  the  face  D. 


FIG.  47 


The  other  ray,  BC,  passes  over  into  the  second  prism  and 
emerges  at  D,  polarized  in  a  horizontal  plane. 

It  has  been  stated  above  that,  in  general,  two  different 
waves  may  be  propagated  in  any  direction.  Theory,  how- 
ever, indicates,  and  experiment  verifies,  that  there  must 
always  be  one,  and  in  some  cases  two,  directions  in  which 
only  a  single  wave  can  pass.  Those  directions  are  called 
the  optic  axes  of  the  crystal,  and  crystals  are  classified 
into  uniaxal  and  biaxal,  according  as  they  have  one  or  two 
of  such  axes.  In  the  first  case  the  arrangement  of  the 
molecules  of  the  crystal  must  be  perfectly  symmetrical 
round  the  axis ;  in  the  second  case  there  is  no  such  perfect 
symmetry  about  any  line.  Theory,  moreover,  does  much 
more  than  indicate  these  general  features ;  it  enables  us  to 
calculate  all  the  details  of  the  wave-motion.  Thus  we  can 
compute  exactly  the  speeds  with  which  waves  will  travel 
in  any  given  direction.  It  is  convenient  to  express  the 


CRYSTALS 


179 


speed  in  terms  of  the  refractive  index,  it  having  been  ex- 
plained before  that  the  speed  is  obtained  by  dividing  a 
known  constant  by  the  refractive  index.  The  results  can 
be  exhibited  in  a  geometrical  form  by  drawing  lines  from 
a  point  0,  the  directions  of  the  lines  indicating  the  direc- 
tion in  which  the  wave  is  traveling  and  the  length  of 
the  line  measuring  its  refractive  index.  If  lines  are  drawn 
in  all  directions  in  this  way,  their  ends  will  all  lie  on  a 
surface,  which  is  called  the  Index  Surface.  Theory  pre- 
dicts the  precise  form  of  this.  In  the  case  of  uniaxal 


FIG.  48 


crystals,  where  there  is  perfect  symmetry  about  an  axis, 
the  index  surface  consists  of  a  sphere  and  a  spheroid, 
with  the  optic  axis  as  a  common  diameter.  A  spheroid  is 
an  egg-shaped  surface  with  perfect  symmetry  about  an 
axis,  so  that  you  may  think  of  the  index  surface  for  a 
uniaxal  crystal  as  being  made  up  of  an  egg  and  a  sphere. 
You  will  realize  at  once  that  the  surface  might  have  two  dis- 
tinct forms :  the  sphere  might  be  inside  the  egg  (Fig.  48  a), 
or  the  egg  might  be  inside  the  sphere  (Fig.  48  b).  The 
crystals  will  have  different  optical  properties  in  the  two 
cases,  and  those  of  the  first  type  are  called  positive  crystals, 
those  of  the  second  negative  crystals.  You  will  see  from 


180  LIGHT 

the  figure  that  a  line  drawn  in  any  other  direction  than 
the  optic  axis  OA  will  cut  the  index  surface  at  two  dif- 
ferent distances  from  the  center  0,  when  it  crosses  the 
sphere  and  the  spheroid  respectively.  These  two  distances 
represent  the  refractive  indices  (and  so  measure  the  speeds) 
of  the  two  waves  that,  we  have  seen,  can  be  propagated 
in  any  direction.  You  will  notice  that  the  law  which 
connects  the  refractive  index  with  the  direction  of  propa- 
gation is  quite  different  for  the  two  waves.  With  the 
sphere  the  radius  is  everywhere  the  same,  so  that  for  the 
corresponding  wave  the  refractive  index  is  the  same  in 
all  directions.  This  is  the  case  with  ordinary  non-crystal- 
line substances,  so  that  the  ray  obeys  the  ordinary  laws  of 
refraction  already  discussed,  and  is  consequently  called  the 
ordinary  ray.  This  deduction  from  theory,  according  to 
which  one  of  the  rays  in  a  uniaxal  crystal  should  obey  the 
ordinary  laws  of  refraction,  has  been  completely  verified 
by  experiment.  Very  careful  estimates  of  the  refractive 
indices  have  been  made  for  waves  in  all  directions,  and  it 
is  found  that  the  refractive  index  is  absolutely  constant, 
or  more  strictly,  the  variations  in  its  measurement  never 
exceeded  0.00002,  a  variation  well  within  the  limits  of  the 
probable  errors  of  the  experiments  that  were  made. 

So  much  for  one  of  the  waves  within  a  uniaxal  crystal. 
With  the  other  wave  and  its  corresponding  ray  the  law 
of  refraction  is  less  simple,  and  as  the  ordinary  law  is  not 
obeyed,  the  ray  is  called  the  extraordinary  ray.  As  you 
see  from  Fig.  48,  the  length  of  the  line  drawn  from  the 
centre  0  to  the  surface  of  the  spheroid  varies  with  the 
direction  of  the  line,  so  that  the  refractive  index  varies 
with  the  direction  of  propagation  of  the  wave.  It  is  a 
simple  problem  of  geometry  to  compute  its  value  for  any 


CRYSTALS 


181 


direction,  making  a  known  angle  6  with  the  optic  axis. 
The  following  table  shows  a  comparison  between  theory 
and  observation  for  the  refractive  index  (n)  correspond- 
ing to  different  directions  (6}.  It  will  be  seen  that  the 
agreement  is  excellent,  the  differences  being  of  the  order 
of  the  probable  errors  of  experiment :  — 


0 

n 
(THEORY) 

n 
(EXPERIMENT) 

9 

n 
(THEORY) 

n 
(EXPERIMENT) 

0°  2'  40" 

1.66779 

1.66780 

46°  46'  2" 

1.56645 

1.56653 

4°  19'  58" 

1.66660 

1.66663 

49°  23'  10" 

1.55861 

1.55876 

7°  51'  58" 

1.66387 

1.66385 

52°  42'  6" 

1.54902 

1.54914 

11°  23'  12" 

1.65967 

1.65978 

58°  39'  10" 

1.53303 

1.53312 

17°  8'  26" 

1.64987 

1.64996 

61°  39'  33" 

1.52570 

1.52573 

20°  26'  1" 

1.64279 

1.64287 

63°  9'  6" 

1.52228 

1.52241 

23°  50'  45" 

1.63451 

1.63455 

66°  14'  27" 

1.51579 

1.51571 

25°  49'  35" 

1.62934 

1.62930 

72°  18'  55" 

1.50476 

1.50475 

29°  18'  42" 

1.61965 

1.61974 

75°  36'  18" 

1.50009 

1.50005 

34°  48'  0" 

1.60336 

1.60336 

79°  6'  26" 

1.49612 

1.49610 

35°  58'  47" 

1.59048 

1.59058 

80°  14'  4" 

1.49507 

1.49507 

40°  49'  21" 

1.58478 

1.58487 

87°  6'  40" 

1.49112 

1.49114 

45°  45'  57" 

1.57000 

1.57014 

89°  49'  6" 

1.49074 

1.49074 

These  results  have  reference  to  uniaxal  crystals  which 
are  perfectly  symmetrical  about  a  line.  With  biaxal 
crystals  there  is  no  such  symmetry,  and  the  optical  proper- 
ties are  consequently  more  difficult  to  deal  with.  How- 
ever, the  same  general  principles  lead  to  a  complete  solu- 
tion of  the  problem,  although  the  results  are  much  less 
simple.  The  index  surface  no  longer  consists  of  a  sphere 
and  a  spheroid,  but  of  two  sheets  that  are  less  familiar  in 
form.  Its  geometrical  properties  can  be  investigated 
mathematically  and  the  values  of  the  refractive  indices 
for  waves  in  any  given  direction  easily  computed.  The 


182 


LIGHT 


following  table,  corresponding  to  that  just  given  for  a 
uniaxal  crystal,  compares  theory  and  experiment  for  a 
number  of  different  directions  in  a  biaxal  crystal.  In  this 
table  r&!  is  the  refractive  index  corresponding  to  the  inner 
sheet  of  the  index  surface,  while  n2  represents  the  same 
quantity  for  the  outer  sheet:  — 


f 

"i 

(THEOEY) 

»i 

(EXPERIMENT) 

1 

«, 

(THEOEY) 

«2 

(EXPERIMFNT) 

0 

1.68103 

1.68099 

0 

1.68533 

1.68526 

3°  12'  50" 

1.67714 

1.67721 

7°  9'  10" 

1.68465 

1.68454 

13°  6'  20" 

1.66298 

.66300 

17°  2'  40" 

1.68445 

1.68448 

21°  4'  30" 

1.64607 

.64603 

25°  0'  50" 

1.68443 

1.68452 

28°  14'  10" 

1.62824 

1.62807 

32°  10'  30" 

1.68443 

1.68447 

35°  29'  20" 

1.60900 

.60897 

38°  27'  30" 

1.68444 

1.68453 

45°  14'  50" 

1.58363 

1.58365 

49°  13'  0" 

1.68445 

1.68457 

60°  1'  30" 

1.55154 

.55157 

63°  59'  30" 

1.68447 

1.68452 

69°  37'  40" 

1.53784 

1.53774 

73°  35'  50" 

1.68448 

1.68444 

When  we  wish  to  estimate  the  velocities  of  the  waves 
that  can  travel  through  a  crystal  in  any  direction,  it  is 
convenient,  as  has  been  seen,  to  know  something  of  the 
form  of  the  Index  Surface  for  the  crystal  in  question. 
There  is,  however,  another  surface  which  is  referred  to 
perhaps  even  more  frequently  in  discussions  of  the  optical 
properties  of  crystals.  This  surface  is  known  as  the  Wave 
Surface,  and  we  must  try  to  realize  what  is  its  significance. 
If  you  throw  a  stone  into  a  pool  and  watch  the  waves 
spreading  outward,  you  will  have  no  difficulty  in  observ- 
ing the  position  of  the  crest  of  the  moving  wave  at  the 
end  of  any  time,  such  as  a  second.  As  the  wave  moves 
out  with  the  same  speed  in  all  directions,  the  crest  will 
form  a  circle  round  the  original  point  of  disturbance  as 


CRYSTALS  183 

center.  If,  instead  of  dealing  with  surface  waves,  you  had 
waves  that  spread  out  in  all  directions  with  equal  veloci- 
ties, then  it  is  clear  that  after  a  second  the  crests  would 
all  lie  on  a  sphere.  This,  then,  is  the  wave  surface  for  a 
uniform  medium,  the  surface  that  contains  the  crests  of 
all  the  waves  that  have  been  moving  outwards  for  a  given 
time,  such  as  a  second.  In  a  crystal  the  waves  move 
with  different  speeds  in  different  directions,  so  that  the 
wave  surface  is  no  longer  spherical.  Its  form  can  be  de- 
termined from  theory,  and  its  geometrical  properties  dis- 
cussed as  fully  as  may  be  desired.  As  there  are  two 
waves  in  any  given  direction,  the  wave  surface  consists  of 
two  sheets,  as  does  the  index  surface,  and,  just  as  with 
that  surface,  its  form  is  specially  simple  for  a  uniaxal 
crystal.  In  that  case  the  wave  surface  is  made  up,  like 
the  index  surface,  of  a  sphere  and  a  spheroid,  as  shown  in 
Fig.  48,  with  the  difference,  however,  that  (a)  is  the  wave 
surface  for  a  negative,  and  (6)  for  a  positive  crystal. 

A  knowledge  of  the  form  of  the  wave  surface  is  very 
helpful  when  dealing  with  the  optical  behavior  of  a  crystal. 
It  enables  you,  for  example,  to  determine  the  directions 
of  the  rays  corresponding  to  waves  in  a  given  direction 
and  to  exhibit  by  a  simple  geometrical  construction  the 
directions  of  polarization  in  the  two  waves.  The  theory 
shows  that  a  ray  is  represented  by  the  line  drawn  from 
the  center  of  the  wave  surface  to  the  point  of  contact  with 
this  surface  of  a  plane  which  touches  it,  and  is  parallel  to 
the  front  of  the  advancing  wave.  I  hold  in  my  hand  an 
apple,  and  will  suppose  for  the  sake  of  illustration  that  it 
represents  a  wave  surface.  In  my  other  hand  I  have  a 
sheet  of  paper,  and  I  shall  take  this  to  represent  the  front 
of  a  wave  of  light  moving  through  the  crystal.  The  direc- 


184  LIGHT 

tion  of  this  wave-front  being  known,  the  problem  before 
me  is  to  determine  the  direction  of  the  corresponding  ray 
of  light.  Move  the  sheet  of  paper  parallel  to  itself  until 
it  touches  the  apple  at  P;  then,  according  to  the  theory, 
if  0  be  the  center  of  the  apple,  corresponding  to  the  center 
of  the  wave  surface,  OP  is  the  direction  of  the  ray.  In 

reality,   of   course,   the 
wave  surface  differs  very 
—+    /g~~ obviously  from  the  sur- 


face of  an  apple.     It  has 

pj  symmetry  about  a  point 

0,  its  center,  and  it  con- 
sists of  two  sheets,  so  that 
planes  in  a  given  direc- 
tion (both  perpendicular 
to  a  given  line  ON)  will 
touch  it  at  two  points, 
P1  and  P2  (one  on  each 
FIG<  49  sheet),  on  the  same  side 

of  the  center  0  (Fig.  49). 

In  this  figure  the  curves  A1P1B1  and  ^L2P2J52  represent 
portions  of  plane  sections  of  the  two  "sheets,"  as  they 
are  called,  of  the  wave  surface.  OP1  and  OP2  represent 
the  two  rays  for  waves  propagated  in  the  direction  ON, 
and  it  should  be  understood  that  the  three  lines  ON,  OP1} 
and  OP2  are  not,  in  general,  in  the  same  plane. 

If  you  will  return  for  a  moment  to  the  case  of  this  apple, 
you  will  see  that  as  I  move  the  sheet  of  paper  in  different 
directions  it  touches  the  apple,  as  a  rule,  just  in  one  point. 
However,  there  is  one  striking  exception  to  this  general 
rule.  Now  I  hold  the  paper  at  right  angles  to  the  stem 
of  the  apple,  and  you  observe  that  it  touches  the  apple 


CRYSTALS  185 

not  in  a  single  point,  but  in  an  infinite  number  of  points 
encircling  the  stem.  The  apple,  as  has  already  been  re- 
marked, is  very  different  in  form  from  the  wave  surface, 
but  the  two  surfaces  have  some  points  of  similarity.  If 
you  were  to  make  a  model  of  the  wave  surface,  you  would 
find  that  it  has  four  points  that  closely  resemble  that  on 
an  apple  near  the  stem  (singular  points  is  their  technical 
name),  and  that  a  plane  that  touches  the  surface  in  the 
neighborhood  of  one  of  these  points  touches  it  not  at  an 
isolated  point,  as  is  the  general  rule,  but  at  an  infinite 
number  of  points  forming  a  circle  round  the  singular 
point.  It  should  still  be  true  that  a  line  drawn  from  the 
center  of  the  wave  surface  to  any  one  of  these  points 
where  the  plane  touches  the  surface  should  represent  a 
ray  of  light  corresponding  to  a  wave-front  parallel  to  the 
plane  in  question.  All  the  lines  drawn  thus  from  the 
center  to  the  various  points  of  contact  will  form  a  cone, 
so  that  we  should  expect  that  if  we  could  get  a  wave  of 
light  to  travel  in  the  right  direction  in  a  crystal,  we  should 
see  not  two  rays  only,  as  in  the  ordinary  case  of  double 
refraction,  but  a  whole  cone  of  rays.  That  this  phenome- 
non was  to  be  expected  was  first  suggested  from  theo- 
retical considerations  such  as  have  just  been  indicated. 
The  theory  was  developed  by  Sir  W.  Hamilton,  and,  at  his 
instigation,  was  put  to  the  test  of  experiment  by  Lloyd. 
Knowing  what  to  look  for,  Lloyd  had  not  much  difficulty 
in  observing  this  phenomenon,  and  it  is  now  well  known 
under  the  name  of  Conical  Refraction.  With  the  crystal 
used  by  Lloyd,  Hamilton's  theory  indicated  that  the 
angle  of  the  cone  of  rays  formed  in  this  way  should  be 
1°  55',  and  Lloyd's  measurements  made  it  1°  50',  the  agree- 
ment being  as  close  as  could  be  expected  in  the  determina- 


186  LIGHT 

tion  of  such  a  quantity.  Here,  then,  we  have  an  example 
of  something  whose  existence  had  never  been  suspected 
until  the  theory  of  light  suggested  the  search  for  it.  Much 
has  been  made  of  this  prediction  from  theory,  perhaps  too 
much.  We  have  already  seen  far  more  wonderful  agreement 
between  theory  and  observation  in  other  fields  of  optics, 
the  only  peculiarity  of  this  case  being  that  the  theory 
came  before  the  observation  and  not  vice  versa.  How- 
ever, it  should  be  remembered  that  the  one  aim  of  the 
theory  is  to  fit  the  facts,  and  it  makes  little  difference 
to  the  value  of  the  theory  whether  the  facts  happen  to 
have  been  previously  observed  or  not.  This  may  be 
largely  a  matter  of  accident,  and  the  only  advantage  that 
can  be  claimed  for  a  theory  that  predicts  the  unknown  is 
that  its  power  to  do  so  should  inspire  extra  confidence, 
seeing  that  the  theory  cannot  have  been  suggested  by 
this  fact  that  is  being  explained,  as  is  often  the  case  with 
"explanations." 

In  a  previous  lecture  we  saw  how  successfully  the  theory 
of  light  can  deal  with  the  problem  of  reflection  and  refrac- 
tion at  the  surface  of  a  non-crystalline  medium  such  as 
glass  or  water.  It  is  equally  successful  in  its  treatment 
of  crystals.  Once  the  general  laws  of  wave  propagation 
in  such  media  are  understood,  there  is  no  special  diffi- 
culty in  proceeding  by  means  of  dynamical  principles  to 
calculate  the  amplitudes  and  phases,  as  well  as  the  direc- 
tions and  velocities,  of  the  various  waves  that  may  arise. 
Of  course,  the  mathematical  processes  are  more  complex 
than  when  we  are  dealing  with  non-crystalline  substances, 
but  all  the  difficulties  that  present  themselves  have  been 
overcome.  Just  a  few  of  the  results  may  be  referred  to 
here,  in  so  far  as  they  can  be  tested  by  experiment. 


CRYSTALS 


187 


We  have  seen  that,  with  a  non-crystalline  substance,  if 
light  be  incident  at  a  certain  angle,  an  angle  that  goes  by 
the  name  of  the  polarizing  angle,  the  reflected  light  has  the 
peculiarity  of  being  plane  polarized.  The  position  of  this 
angle  for  any  substance  is  easily  determined  from  the 
simple  law,  due  to  Brewster,  that  the  tangent  of  the  angle 
is  equal  to  the  refractive  index  of  the  substance.  In  the 
case  of  crystals,  theory  indicates  that  there  will  also  be  a 
polarizing  angle,  but  that  the  law  from  which  it  may  be 
computed  is  less  simple.  With  crystals  the  refractive 
index  is  not  a  constant,  but  depends  on  the  direction  in 
which  the  wave  is  being  propagated  and  the  nature  of 
its  polarization.  We  should  expect,  therefore,  that  the 
polarizing  angle  would  depend  on  these  things,  and  in  this 
theory  and  observation  agree.  The  following  table  gives 
a  comparison  between  theory  and  observation  as  to  the 
values  of  the  polarizing  angle  under  different  circum- 
stances of  reflection  from  a  uniaxal  crystal.  The  angle  is 
different  according  as  the  plane  of  incidence  is  parallel  or 
perpendicular  to  the  plane  containing  the  optic  axis  of 
the  crystal.  These  two  cases  are  distinguished  by  sub- 
scripts; thus,  P1  and  P2.  The  angle  0  is  the  angle  that 
the  optic  axis  makes  with  the  reflecting  face  of  the  crystal. 
The  results  are  shown  graphically  in  Fig.  50 :  — 


e 

.0°  25' 

27°  2' 

45°  29' 

64°  1'  30" 

89°  47' 

Pi  (theory)  .     .     . 

54°  3' 

55°  25' 

57°  25' 

59°  25' 

60°  41' 

PI  (experiment)    . 

54°  12' 

55°  26' 

57°  22' 

59°  19' 

60°  33' 

P2  (theory)  .     .     . 

58°  55' 

59°  17' 

59°  48' 

60°  23' 

60°  41' 

P2  (experiment)    . 

58°  56' 

59°  4' 

59°  48' 

60°  75' 

60°  33' 

188 


LIGHT 


In  the  case  of  reflection  from  a  non-crystalline  substance 
we  have  seen  that  at  the  polarizing  angle  the  reflected 
light  is  polarized  in  a  plane  parallel  to  the  plane  of  inci- 


56 


^Q  10°     20°     30°     40°     50°     60°     70°     80°     90 
FIG.  50 

dence.  With  a  crystal,  however,  this  is  not  the  case. 
The  plane  of  polarization  deviates  from  that  of  incidence, 
being  inclined  to  it  at  a  small  angle,  A,  which  can  be  cal- 
culated from  theory.  The  values  of  A  obtained  from 
theory  and  experiment  were  as  follows,  for  the  case  of 
reflection  from  a  uniaxal  crystal  whose  optic  axis  was 
parallel  to  the  reflecting  surface.  The  angle  a  denotes 
the  angle  between  the  optic  axis  and  the  plane  of  incidence. 


a 

0° 

23°  30' 

45° 

67°  30' 

90° 

A  (theory)  .... 

0 

2°  46' 

3°  54' 

2°  46' 

0 

A  (experiment)    .     . 

0 

2°  46' 

3°  57' 

2°  43' 

0 

When  dealing  with  ordinary  reflection,  we  made  a  com- 
parison between  theory  and  observation  as  to  the  differ- 
ence of  phase  between  two  reflected  waves  which  are 


CRYSTALS 


189 


polarized  respectively  parallel  and  perpendicular  to  the 
plane  of  incidence.  The  corresponding  problem  for  crystal- 
line reflection  is  more  complex,  but  the  general  character 
of  the  results  is  the  same.  This  will  be  seen  at  once  by 
comparing  Fig.  51,  which  shows  how  the  difference  of 


0.5 


0.4 


0.3 


0.2 


I 


55° 


57 c 


58 c 


59° 
FIG.  51 


62° 


phase  depends  upon  the  angle  of  incidence  in  reflection 
from  a  crystal,  with  Fig.  32  of  the  earlier  lecture. 

In  this,  as  in  some  other  lectures,  I  have  brought  before 
your  notice  a  number  of  tables  and  figures  that  will  prob- 
ably prove  attractive  or  repellent  according  to  the  degree 
in  which  you  realize  their  significance.  Their  object  in  all 
cases  is  to  show  how  well,  or  how  ill,  the  theory  fits  the 
facts,  and  I  hope  that  by  this  time  their  cumulative  effect 
will  have  convinced  you  that  the  modern  theory  of  light 
keeps  always  very  close  to  the  solid  ground  of  fact.  Such 
things  are  full  of  interest  to  a  serious  scientist,  as  they 


190  LIGHT 

give  him  what,  above  all,  he  is  anxious  to  have,  a  search- 
ing test  of  his  theories;  but  the  optical  effects  with  which 
they  deal  do  not  make  a  very  wide  appeal.  They  would 
not  usually  be  described  as  beautiful,  and  few  men,  out- 
side the  narrow  circle  of  the  physicists,  would  display 
much  enthusiasm  over  tables  of  refractive  indices,  polariz- 
ing angles,  and  the  like.  It  happens,  however,  that  with 
crystals  we  can  produce  effects  that  are  generally  recog- 
nized as  extremely  beautiful,  and  that  the  careful  observa- 
tion of  some  of  these  also  serves,  in  a  measure,  as  a  test 
of  the  accuracy  of  our  theory  of  the  propagation  of  light 
in  a  crystal.  You  are  aware, 'perhaps,  that  if  you  make  a 
solution  of  tartaric  acid,  pour  it  over  glass,  and  evaporate 
the  water  by  means  of  a  steady  heat,  you  may,  with  proper 
precautions,  get  a  film  of  minute  crystals  of  the  acid  de- 
posited on  the  glass.  Here  is  a  glass  disk  upon  which  is 
such  a  deposit.  I  place  it  between  these  two  NicoFs 
prisms,  and  allow  the  bright  light  from  the  lantern  to 
shine  through  the  apparatus.  If  you  direct  your  attention 
to  the  screen,  you  will  admit,  at  any  rate,  that  the  colors  are 
very  gorgeous,  and  probably  that  the  picture  is  a  beautiful 
one.  Its  beauty  is  enhanced  by  its  irregularity,  and  this 
is  due  to  the  fact  that  the  little  crystals  on  the  glass  pre- 
sent their  facets  to  the  light  at  angles  of  all  sorts.  There 
is  thus  a  total  absence  of  that  mathematical  precision 
which  is  the  only  objection  that  can  be  brought  against 
the  claim  of  beauty  made  on  behalf  of  the  phenomena 
with  which  we  are  to  be  occupied  during  the  remainder 
of  this  lecture. 

These  phenomena  are  all  produced  by  interposing  a 
thin  crystalline  plate  between  two  Nicols.  The  effect  of 
each  Nicol  is  to  confine  the  vibrations  to  a  definite  plane, 


CRYSTALS 


191 


so  that  the  light  that  gets  through  a  Nicol  must  be  plane 
polarized  in  a  direction  that  depends  on  the  way  in  which 
the  Nicol  is  turned.  The  effect  of  the  plate  of  crystal  is 
to  split  up  the  incident  wave  of  light  into  two  waves, 
moving  forward  with  different  speeds.  By  the  time  that 
these  two  waves  have  traversed  the  crystal,  they  will  have 


FIG.  52 


got  out  of  phase,  and  if  their  difference  of  phase  be  of  the 
right  amount,  then,  as  we  saw  in  the  last  lecture,  they 
will  interfere  and  in  combination  produce  darkness.  If  we 
arrange  things  so  that  at  different  points  of  the  plate  the 
difference  of  phase  between  the  emerging  waves  is  dif- 
ferent, then  there  will  be  interference  at  some  points  and 
not  at  others,  so  that  we  shall  get  alternations  of  light  and 
darkness.  It  is  easy  to  see  that  if  the  incident  beam  be 
parallel,  we  shall  have  no  such  alternations,  but  uniform 
brightness  (or  darkness)  over  the  plate.  If  AB  (Fig.  52) 
represent  the  front  of  a  wave  falling  on  the  plate,  this 
will  set  up  two  waves  moving  with  different  velocities, 
and  these  will  emerge  from  the  plate  with  a  difference  of 
phase  represented  by  ef  in  the  figure.  If  A'B'  and  A"B" 


192 


LIGHT 


be  other  wave-fronts,  the  phase  differences  on  emergence 
will  be  e'f  and  e"ff  respectively.  Now  it  is  obvious  that 
if  A'E'  be  parallel  to  AB,  as  will  be  the  case  if  the  incident 
beam  be  parallel,  then  e'f  will  be  equal  to  ef.  Thus  the 
phase  difference  in  the  neighborhood  of  Cr  will  be  the  same 
as  that  at  C,  and  it  will  be  equally  bright  at  these  two 


FIG.  53 


points.  If,  then,  we  want  alternations  of  light  and  dark- 
ness, we  must  abandon  a  parallel  incident  beam. ,  If  we 
arranged  that  the  incident  beam  should  diverge  from  or 
converge  to  a  point,  as  indicated  in  Fig.  53,  then  any  two 
wave-fronts  would  not  be  parallel,  but  would  be  inclined 
to  one  another,  as  represented  by  AB  and  A"B"  in  Fig.  52. 
The  differences  of  phase  on  emergence  would  be  ef  and 
e"f" ,  and  as  these  are  different  it  might  be  bright  at  C 
and  dark  at  C". 

We  shall  suppose  that  things  are  arranged  to  avoid  a 
parallel  beam,  and  that  the  incident  pencil  of  light  is  of 
a  diverging  or  converging  character,  with  OQ  for  its  axis. 
We  shall  then  examine  the  simplest  case  that  can  be  pre- 
sented, that  of  perfect  symmetry,  where  we  have  a  uni- 


CRYSTALS 


193 


axal  crystal,  the  plate  of  which  is  cut  at  right  angles  to 
the  optic  axis,  the  direction  of  this  axis  coinciding  with 
that  of  the  incident  pencil.  If  we  were  to  look  down  upon 
the  plate  in  the  direction  of  the  axis,  and  observe  a  plan 
of  the  mechanical  analogue  referred  to  on  pp.  101  and  177, 
then,  as  there  must  be  perfect  symmetry  about  the  axis, 
the  arrangement  of  the  obstacles  would  be  that  repre- 
sented in  Fig.  54  a.  At  any  point,  Ply  the  vibrations 


(a) 


FIG.  54 


must  be  confined  to  one  or  other  of  two  directions,  P±R 
and  P!$,  at  right  angles  to  one  another.  Of  these  the 
first,  PiR,  is  along  the  direction  QPi,  and  the  second  is  at 
right  angles  to  this.  Now  suppose  that  the  first  Nicol  is 
so  placed  that  it  stops  all  vibrations  except  those  parallel 
to  QNl  (Fig.  54  6).  Then  PjT7,  which  is  parallel  to  QN1} 
may  represent  a  displacement  in  the  incident  wave  as  it 
strikes  the  crystal  plate.  Before  considering  what  happens 
to  the  'wave  within  the  crystal,  it  is  convenient  to  "  re- 
solve" the  displacement  P177into  its  equivalent,  P^R  com- 
bined with  P!$,  or  what  is  the  same  thing,  P±R  combined 
with  RT.  It  will  be  seen  that  RT  is  equal  and  parallel 
to  P!$,  so  that  these  two  lines  represent  displacements  of 
the  same  magnitude  and  in  the  same  direction.  [This 


194  LIGHT 

" resolution"  of  a  displacement  P^T  into  two  displace- 
ments, P^R  and  RT,  according  to  the  "  triangle  law/'  is 
really  a  very  simple  matter,  it  being  obvious  that  the  final 
displacement  is  the  same,  whether  you  go  direct  from  Pl  to 
T,  or  by  two  stages  from  Pl  to  R,  and  then  from  R  to  T.] 
Instead,  then,  of  saying  that  in  the  incident  wave  there  is 
a  displacement  P{F  parallel  to  QNlf  we  may  say  that 
there  are  two  displacements,  one,  P-JI,  being  in  the  direc- 
tion QPV  and  the  other,  RT,  at  right  angles  to  this.  Dis- 
placements in  the  first  of  these  directions  are  characteristic 
of  one  of  the  waves  that  the  crystal  can  transmit,  while 
displacements  in  the  other  characterize  the  second  wave. 
These  two  waves,  as  we  have  seen,  traverse  the  crystal 
with  different  speeds,  and  emerge  with  a  difference  of 
phase.  What  this  phase  difference  is  will  depend,  as  ap- 
pears from  Fig.  52,  on  the  angle  at  which  the  incident 
wave  strikes  the  face  of  the  crystal.  This  will  be  the 
same  for  all  points  Pl  that  are  at  the  same  distance  from 
the  axis  Q,  but  will  be  different  at  different  points  along 
the  line  QP.  Let  us  suppose  that  the  point  PI  is  so  placed 
that  the  phase  difference  is  one  wave-length  for  the  color 
under  consideration.  How  will  the  two  waves  of  light  of 
this  color  combine  after  they  pass  through  the  second 
Nicol?  That,  of  course,  will  depend  upon  the  position 
of  this  Nicol.  Let  us  suppose  that  the  two  Nicols  are 
"  crossed,"  so  that  the  second  Nicol  stops  all  vibrations 
except  those  in  the  direction  QN2  (Fig.  54  b),  where*  A^QA^ 
is  a  right  angle.  Draw  R U  (Fig.  55)  parallel  to  QN2  and 
therefore  perpendicular  to  P^T  or  QNi.  The  displacement 
represented  by  P-JH  is  equivalent  to  a  combination  of 
two  displacements,  represented  in  magnitude  and  direction 
by  Pa£7  and  UR  respectively.  The  displacement  Pj£7  is, 


CRYSTALS 


195 


however,  annulled  by  the  second  Nicol,  which  will  not 
permit  a  wave  to  pass  unless  the  displacements  therein 
are  parallel  to  QN2.  We  see  then  that,  while  PiR  repre- 
sents the  displacement  in  one  of  the  waves  that  emerges 
from  the  plate  of  crystal,  after  this  wave  has  traversed 
the  second  Nicol  the  displacement  is  changed  to  UR. 
The  displacement  in  the  other  wave,  represented  byRT, 
may  be  dealt  with  similarly.  It  is  equivalent  to  two 
displacements, 
RU  and  UT, 
and  of  these 
the  second  is 
annulled  by  the 
Nicol,  so  that 
the  displace- 
ment in  this 
wave  as  it  comes 
through  the 

Nicol  is  RU.  Now  we  have  supposed  that  P1  is  so 
situated  that  the  difference  of  phase  between  the  two 
waves  is  exactly  a  wave-length,  and  this/  as  far  as  optical 
effects  are  concerned,  is  the  same  as  if  the  waves  were 
in  the  same  phase.  We  have  thus  to  combine  two  waves 
that  arc  in  the  same  phase,  the  displacements  in  which  are 
so  related  that  one  is  represented  by  UR  and  the  other  by 
the  exactly  equal  and  opposite  RU.  Clearly  these  two 
displacements  annul  one  another,  so  that  the  color  cor- 
responding to  this  particular  wave-length  is  totally  absent 
from  Pj.  As  everything  is  symmetrical  round  the  axis, 
this  absence  of  color  will  apply  to  all  points  on  a  circle 
whose  radius  is  QPl  and  center  is  Q,  so  that  there  will 
be  a  dark  circle  round  the  axis.  The  argument  will  apply 


FIG.  55 


196 


LIGHT 


FIG.  56 


equally  well  to  a  point  P2  so  chosen  that  the  phase  differ- 
ence is  two  wave-lengths,  or  to  P3,  where  it  is  three  wave- 
lengths, and  so  on.  Thus 
there  will  be  a  whole  series 
of  circles  round  the  axis, 
which  will  be  dark  as  far 
as  the  color  corresponding 
to  this  wave-length  is  con- 
cerned. 

These  concentric  circles 
will  not,  however,  be  the 
only  dark  regions  of  the 
field  of  view.  Consider 
any  point  P  (Fig.  54)  on 
the  line  QNV  The  only 
displacement  at  such  a  point  that  the  first  Nicol  will  per- 
mit to  pass  must  be  in  the  direction  QN^  and  as  this  is 
at  right  angles  to  QN2,  the 
corresponding  wave  will 
not  be  able  to  get  through 
the  second  Nicol.  There 
must,  therefore,  be  com- 
plete darkness  at  P,  and  so 
for  any  other  point  on  lines 
in  the  directions  QNl  and 
QN2.  Hence,  we  should 
expect  to  see  a  series  of 
dark  circles  round  the  axis, 
with  a  black  cross  whose 
arms  are  parallel  to  the  di- 
rections QN1  and  QN2  such  as  is  represented  in  Fig.  56. 
The  difference  of  phase  for  the  two  waves  that  traverse 


FIG.  57 


CRYSTALS  197 

the  crystal  depends  on  the  velocities  of  these  waves,  and  so  is 
different  for  waves  of  different  length  and  color.  Thus,  the 
points  P-f^..  will  have  slightly  different  positions  for 
the  different  colors  that  go  to  make  up  white  light, 
and  if  the  incident  light  be  of  this  character,  the  rings 
will  be  colored,  giving  the  beautiful  effect  that  you 
now  see  on  the  screen.  Figure  57  is  from  a  photograph 
of  what  actually  appears,  unfortunately,  however,  robbed 
of  all  the  beauty  of  color.  You  will  observe  that  the 
darkest  part  of  the  field  corresponds  exactly  with  the 
cross  and  rings  predicted  from  theory  and  indicated  in 
Fig.  56. 

We  have  been  dealing  with  the  case  in  which  the  two 
Nicols  are  "  crossed."  Suppose,  now,  that  we  turn  the 
second  Nicol  through  a  right  angle,  so  that  QN2  of  Fig.  54 
coincides  with  QNl}  and  consider  in  what  way  this  should 
modify  the  results.  As  before,  the  displacement  repre- 
sented by  P!#  is  equivalent  to  a  combination  of  P-JJ  and 
UR  (Fig.  55),  but  of  these  it  is  the  second  that  is  now 
annulled  by  the  second  Nicol,  so  that  when  this  wave 
gets  through  the  apparatus  the  displacement  in  it  is  repre- 
sented in  magnitude  and  direction  by  Pfl.  In  the  other 
wave  the  displacement  RT  is  again  equivalent  to  RU 
combined  with  UT,  and  the  first  of  these  is  annulled  by 
the  second  Nicol,  so  that  UT  represents  the  displacements 
in  the  emergent  wave.  Thus  the  displacements  in  the 
two  waves  are  in  the  same  direction,  and  being  effectively 
in  the  same  phase,  their  combined  effect  is  additive,  and 
instead  of  darkness  we  have  brightness.  Thus,  where 
formerly  we  had  a  series  of  dark  rings  we  should  now 
expect  a  complementary  series  of  bright  ones.  The  cross, 
too,  instead  of  being  black,  will  be  bright.  For  if  we  take 


198 


LIGHT 


a  point  such  as  P  on  QN^  the  first  Nicol  confines  its 
displacements  to  the  direction  QN^  and  these  pass  freely 
through  the  second  Nicol,  and  this  is  true  also  for  a  point 
on  a  line  at  right  angles  to  QNr  Thus  we  have  brightness 
all  along  two  lines  at  right  angles,  as  you  see  from  Fig.  58, 
which  represents  the  actual  state  of  affairs,  except,  as 

before,  for  the  color. 

In  dealing  with  these 
phenomena  of  rings  and 
crosses,  I  have  attempted 
merely  to  indicate  the 
general  character  of  the 
results  that  are  to  be  ex- 
pected and  that  are  ac- 
tually found  to  occur. 
With  the  aid,  however,  of 
the  theory  of  wave  prop- 
agation in  a  crystal,  it  is 
not  difficult  to  predict 
more  of  the  details  of  the  phenomena,  such  as  the  size 
and  relative  intensity  of  the  rings  as  well  as  their  form. 
A  very  great  number  of  arrangements  of  the  crystalline 
plate  and  the  Nicols  have  been  examined,  both  from  the 
theoretical  and  the  experimental  point  of  view,  and  the 
agreement  between  the  two  is  thoroughly  satisfactory  at 
all  points.  We  have  dealt  only  with  the  simplest  case 
that  can  present  itself,  that  of  a  uniaxal  crystal  cut  at 
right  angles  to  its  optic  axis,  with  the  axis  of  the  incident 
light  in  the  same  direction  as  the  optic  axis.  The  re- 
sults, of  course,  are  more  complex  with  crystals  of  a  less 
simple  form,  and  it  may  suffice  to  refer  very  briefly  to  a 
few  other  cases. 


FIG.  58 


CRYSTALS 


199 


Let  us  take  first  the  case  of  two  thin  plates  of  the  same 
material  and  thickness,  both  cut  with  their  faces  parallel 
to  their  optic  axes,  and  held  together  with  their  axes  at 
right  angles  to  one  another.  Theory  shows  that  in  this 
case  we  should  again  see  a  dark  cross,  and  that  the  other 
dark  lines  in  the  field  should  be  a  series  of  rectangular 
hyperbolas  such  as  are  represented  in  Fig.  59  a.  This 


figure  shows  the  darkest  portion  of  the  field  according  to  the 
theory,  while  Fig.  59  b  is  from  a  photograph  of  what  is 
really  seen. 

Consider  next  a  thin  plate  cut  from  a  biaxal  crystal, 
with  its  faces  at  right  angles  to  the  bisector  of  the  angle 
between  the  optic  axes.  Put  this  plate  between  a  pair  of 
crossed  Nicols,  and  turn  it  so  that  the  line  joining  the 
ends  of  the  optic  axes  is  parallel  or  perpendicular  to  the 
"  principal  planes "  of  the  Nicols,  i.e.  is  parallel  to  lines 
such  as  QN1  or  to  QN2  of  Fig.  54  6.  If  a  beam  of  light 
like  that  used  before  now  fall  upon  the  plate,  we  should 
expect  alternations  of  light  and  darkness.  Investigation 
shows  that  a  black  cross  is  to  be  looked  for  in  this  case 


200 


LIGHT 


as  before;    but  the  other  dark  lines  in  the  field  will  no 
longer  be  circles  or  hyperbolas.     Their  form  is  easily  deter- 


mined  from  theory,  and  it  appears  that  they  belong  to  a 
class  of  curves  known  as  lemniscates,  whose  foci  are  at  the 
ends  of  the  two  optic  axes.  Figure  60  a  shows  the  lines 


drawn  through  the  darkest  part  of  the  field,  according  to 
the  predictions  of  theory.  Figure  60  b  is  from  a  photo- 
graph of  what  is  actually  seen  (except,  once  more,  for  the 


CRYSTALS  201 

color),  and  by  comparing  these  two  figures  you  will  see 
that  there  is  an  excellent  agreement. 

Lastly,  let  us  turn  the  crystalline  plate  through  an 
angle  of  45°  from  its  last  position  and  see  the  change  that 
takes  place.  The  lemniscates  should  appear,  as  before, 
but  turned  through  half  a  right  angle;  and  there  should 
be  no  black  cross,  its  place  being  taken  by  a  dark  hyper- 
bola going  through  the  ends  of  the  optic  axes.  The 
darkest  part  of  the  field,  according  to  theory,  should  appear 
as  in  Fig.  61  a,  and  this  should  be  compared  with  the 
neighboring  figure  (61  b)  from  a  photograph  of  the  actual 
appearance.  These  various  figures  give  no  idea  of  the 
beauty  due  to  the  scheme  of  color;  but  they  may  serve 
their  purpose  of  bringing  home  to  you  with  what  accuracy 
theory  enables  us  to  foretell  what  is  to  be  expected  under 
any  given  circumstances,  and  to  account  for  all  the  de- 
tails of  the  phenomena  that  have  been  observed. 


IX 


DIFFRACTION 

SUPPOSE  you  throw  a  stone  into  water  at  S  (Fig.  62), 
and  watch  what  happens.  A  circular  wave  will  travel  out 
over  the  surface  of  the  water  in  all  directions.  At  one 
time  the  crest  of  the  advancing  wave  will  be  at  OP;  a 

little  later  it  will  have 
moved  on  to  EQ.  How 
\E  is  this  effect  produced? 
The  impact  of  the  stone 
causes  a  disturbance  at 
S,  an  up-and-down 
motion  of  the  water 
there,  and  this  is  com- 
municated to  the  neigh- 
boring particles.  Each 
particle  hands  on  the 

disturbance  to  its  neighbor;  but  in  what  way  does  it 
hand  it  on?  It  looks  somewhat  as  if  the  disturbance 
could  be  passed  along  only  in  one  direction.  P  seems 
to  pass  on  its  motion  only  in  the  direction  Pa,  forwards 
towards  Q,  and  not  backwards  toward  S,  or  laterally 
along  Pb  or  PC  or  Pd.  If  this  were  so,  it  would  appear 
to  explain  some  of  the  phenomena.  Thus,  it  would 
explain  why  there  is  no  disturbance  behind  OP  (in  the 
direction  toward  'S),  and  in  the  case  of  waves  of  light  — 
and  it  is,  of  course,  with  the  analogous  problem  in  light 

202 


FIG.  62 


DIFFRACTION  203 

that  we  are  interested  —  why,  if  we  put  a  screen  in  the 
position  OF,  we  appear  to  get  a  sharply  defined  shadow 
extending  to  E,  where  SOE  is  a  straight  line.  This  familiar 
phenomenon  of  shadows  gave  rise  to  the  idea  that  light 
moves  in  straight  lines,  and,  as  we  have  seen,  the  law  of 
the  rectilineal  propagation  of  light  was  one  of  the  few 
general  laws  of  optics  that  were  known  to  the  world  in  OCA 
pre-Newtonian  days.  The  only  objection  to  the  law  is  ^ 
that  it  is  not  true.  Light  does  not  move  in  straight  lines, 
and  the  shadow  of  an  obstacle  is  not  sharply  defined  by 
drawing  straight  lines  from  the  source  of  light  to  the  edge 
of  the  obstacle.  Closer  examination  reveals  the  fact  that 
light  bends  round  a  corner.  This  phenomenon  was  some- 
times spoken  of  as  the  inflection  of  light,  but  is  now  always 
referred  to  as  diffraction. 

When  we  look  into  the  question  of  the  amount  of  bend- 
ing round  a  corner,  and  discuss  it  by  means  of  the  prin- 
ciples to  be  referred  to  later,  we  find  that  the  bending 
depends  very  largely  on  the  length  of  the  wave,  short  waves 
being  much  less  bent  than  long  ones.  This  dependence 
of  the  bending  on  the  wave-length  is  so  important  that  it 
may  be  well  to  make  an  experiment  to  bring  it  home  to 
you.  In  ordinary  speaking  you  set  up  waves  in  the  air, 
and  you  know  that  these  must  bend  freely,  as  you  can 
easily  hear  a  person  who  is  speaking  round  a  corner.  The 
length  of  the  waves  that  are  thus  set  up  by  speech  de- 
pends on  the  pitch  of  the  voice,  but  we  may  say  that 
normally  they  are  four  or  five  feet  long.  In  my  hand  I 
have  a  whistle  that  will  produce  very  much  shorter  waves 
than  that.  As  it  is  now  arranged  it  sends  out  waves 
about  four  inches  long,  and  by  altering  its  mechanism  I 
can  make  the  waves  shorter  and  shorter.  If  one  of  you 


204  LIGHT 

were  to  go  behind  that  large  screen,  and  listen  carefully 
while  I  sound  the  whistle,  you  might  be  able  to  determine 
whether  there  is  anything  resembling  a  sound  shadow  or 
not.  It  will  be  better,  however,  to  arrange  things  so  that 
all  can  observe  the  phenomena  together.  We  can  do  this 
easily  by  aid  of  this  sensitive  flame  that  you  can  all  see, 
and  that  will  serve  just  as  well  as  an  ear  (indeed,  better 
than  that  in  some  respects)  to  detect  the  presence  of  a 
wave  in  the  air.  The  manner  of  producing  this  sensitive 
flame  need  not  concern  us  at  present,  all  that  need  be 
known  being  that  it  is  sensitive  —  you  observe  that  the 
flame  ducks  when  I  blow  this  whistle  and  the  disturbance  in 
the  air  strikes  it.  For  our  purposes  this  flame  has  the  im- 
portant advantage  over  the  ear  that  it  can  be  made  sensi- 
tive to  waves  that  are  too  short  to  produce  the  sensation 
of  sound.  It  has  already  been  pointed  out  that  the  eye 
is  sensitive  only  to  waves  whose  lengths  lie  within  a  cer- 
tain range,  and  the  same  is  true  of  the  ear.  Very  high 
notes  and  very  low  notes  cannot  be  heard,  as  they  do  not 
affect  the  ear  in  the  right  way,  and  it  should  be  remem- 
bered when  watching  this  experiment  with  the  whistle  and 
the  flame  that  very  high  notes  are  very  short  in  wave  length. 
As  I  alter  the  effective  length  of  this  whistle,  you  can  hear 
that  the  note  it  emits  gets  shriller,  and  now  that  the  wave 
is  so  short  that  you  hear  no  note  at  all,  there  is,  as  you  see, 
a  somewhat  sharply  defined  shadow  of  the  screen.  You 
observe  that  when  I  move  the  whistle  very  slightly  to 
the  right  or  to  the  left  of  a  line  joining  the  sensitive  flame 
to  the  edge  of  the  screen,  there  is  a  perceptible  difference 
in  the  effect.  In  one  case  the  flame  is  inside  the  shadow, 
and  is  unaffected  of  the  waves  in  the  air;  in  the  other  it 
responds  to  the  action  of  these  waves.  You  see,  then, 


DIFFRACTION  205 

that  although  an  ordinary  sound-wave  bends  readily  round 
a  corner,  there  is  scarcely  any  bending  perceptible  when 
the  length  of  the  wave  is  sufficiently  short. 

This  problem  of  the  bending  of  light  round  a  corner  has 
presented  difficulties  almost  from  the  beginning  of  modern 
science.  Newton  knew  some  of  the  phenomena  quite 
well,  but  he  did  not  observe  them  closely  enough  to  grasp 
all  that  was  significant,  and  his  failure  to  do  so  led  him 
seriously  astray.  He  knew  that  the  shadows  of  bodies 
are  bordered  with  colored  fringes.  He  knew  also  that  if 
the  light  from  a  small  source  falls  upon  a  body,  the  shadow 
is  not  exactly  coincident  with  the  geometrical  shadow,  as  it 
is  sometimes  called,  i.e.  the  figure  formed  by  drawing  straight 
lines  from  the  source  of  light  past  the  edge  of  the  opaque 
body  and  observing  where  these  lines  are  interrupted  by 
the  plane  on  which  the  shadow  is  cast.  Thus,  in  his  first 
observation  on  "The  Inflexions  of  the  Rays  of  Light,"  in 
the  third  book  of  his  "  Opticks,"  he  tells  us  that  he  let  light 
stream  through  a  pinhole  in  a  piece  of  lead  and  fall  upon 
various  objects,  and  he  then  observed  that  "the  shadows 
were  considerably  broader  than  they  ought  to  be,  if  the 
rays  of  light  passed  on  by  these  bodies  in  right  (i.e.  straight) 
lines.  And  particularly  a  hair  of  a  man's  head,  whose 
breadth  was  but  the  280th  part  of  an  inch,  being  held  in 
this  light,  at  the  distance  of  about  12  feet  from  the  hole, 
did  cast  a  shadow  which  at  the  distance  of  4  inches  from 
the  hair  was  the  60th  part  of  an  inch  broad,  that  is,  about 
four  times  broader  than  the  hair."  In  this  case  there 
seems  to  be  a  bending  away  from  the  shadow  and  not 
into  it.  This  puzzled  Newton,  and  seemed  to  him  so  in- 
compatible with  a  wave  theory  of  light  that  he  rejected 
that  theory.  Listen  to  what  he  says  in  one  of  his  famous 


206  LIGHT 

queries  at  the  end  of  his  book  on  optics.  "Are  not  all 
hypotheses  erroneous  in  which  light  is  supposed  to  con- 
sist in  motion  propagated  through  a  fluid  medium  ?  If  it 
consisted  in  such  motion,  it  would  bend  into  the  shadow. 
For  motion  cannot  be  propagated  in  a  fluid  in  right  lines 
beyond  an  obstacle  which  stops  part  of  the  motion,  but 
will  bend  and  spread  every  way  into  the  quiescent  medium 
which  lies  beyond  the  obstacle.  The  waves  on  the  surface 
of  stagnating  water  passing  by  the  sides  of  a  broad  obstacle 
which  stops  part  of  them,  bend  afterwards,  and  dilate 
themselves  gradually  into  the  quiet  water  behind  the 
obstacle.  The  waves  of  the  air,  wherein  sounds  consist, 
bend  manifestly,  though  not  so  much  as  the  waves  of 
water.  But  light  is  never  known  to  follow  crooked  pas- 
sages nor  to  bend  into  the  shadow.  For  the  fixed  stars,  by 
the  interposition  of  any  of  the  planets,  cease  to  be  seen. 
And  so  do  the  parts  of  the  Sun  by  the  interposition  of  the 
Moon,  Mercury,  or  Venus.  The  rays  which  pass  very  near 
to  the  edges  of  any  body  are  bent  by  the  action  of  the 
body ;  but  this  bending  is  not  towards  but  from  the  shadow, 
and  is  performed  only  in  the  passage  of  the  ray  by  the 
body,  and  at  a  very  small  distance  from  it.  So  soon  as 
the  ray  is  past  the  body  it  goes  right  on/7  Had  Newton 
varied  his  experiments,  and  observed  carefully  enough,  he 
could  have  found  a  bending  towards  the  shadow,  as  we 
shall  see  later.  Here,  then,  we  have  a  striking  case  of  a 
very  great  scientist  being  led  astray,  and,  as  we  now  see  it, 
very  seriously  astray,  by  experimental  evidence.  Snares 
seem  to  be  laid  along  every  path,  and  we  may  be  en- 
trapped by  experiment  just  as  well  as  by  theory.  There 
are  so  many  warnings  up  along  the  latter  road  that  there 
is  not  the  same  excuse  for  falling.  And  yet  men  fall,  as 


DIFFRACTION  207 

Brewster  did  not  so  very  long  ago,  if  Tyndall  reports  him 
fairly.  "  In  one  of  my  latest  conversations  with  Sir  David 
Brewster,  he  said  that  his  chief  objection  to  the  wave 
theory  of  light  was  that  he  could  not  think  the  Creator 
guilty  of  so  clumsy  a  contrivance  as  the  filling  of  space 
with  ether  in  order  to  produce  light."  Such  a  high  a  priori 
road  is  probably  the  most  dangerous  of  all. 

To  return  to  the  problem  of  diffraction,  there  is  by  this 
time  not  the  slightest  doubt  that  light  does  bend  round  a 
corner.  As  we  shall  see  presently,  we  have  many  care- 
ful determinations  of  the  amount  of  bending  and  of  vari- 
ous details  of  the  phenomena.  With  the  refinements  of 
modern  instruments  at  our  disposal,  it  is  comparatively 
easy  to  deal  with  these  matters  experimentally ;  but  when 
we  come  to  examine  them  from  the  standpoint  of  theory, 
a  number  of  difficulties  arise.  The  form  that  the  problem 
takes  in  the  mind  of  a  mathematical  physicist  is  something 
as  follows.  A  given  disturbance  is  set  up  in  the  ether  by 
the  presence  of  a  source  of  light.  This  spreads  out  in  a 
known  manner,  and  there  is  no  special  difficulty  in  calcu- 
lating and  predicting  all  the  details  of  the  phenomena  to 
be  observed,  provided  that  no  opaque  obstacle  is  present. 
Suppose,  however,  an  opaque  body  is  put  in  the  way  of 
the  waves  in  the  ether.  How  does  this  affect  the  motion 
of  the  waves  in  the  region  beyond  the  body  ?  The  physical 
and  mathematical  conditions  to  be  satisfied  are  easily 
stated.  We  know  the  disturbance  in  the  neighborhood  of 
the  source,  and  we  know  the  conditions  to  be  satisfied  at 
all  points  of  the  boundary  of  the  opaque  obstacle.  It 
looks  as  if  everything  that  we  want  should  be  within  our 
powers  of  computation,  and  in  other  fields  many  similar 
problems  have  been  successfully  attacked.  In  the  case  of 


208  LIGHT 

optics,  however,  peculiar  difficulties  present  themselves 
owing  to  the  extreme  shortness  of  the  waves  of  light,  and 
these  difficulties  have  not  as  yet  been  successfully  over- 
come, except  in  a  few  very  special  cases.  In  general,  the 
complete  solution  of  the  optical  problem  of  diffraction  still 
awaits  us.  I  trust  that  you  do  not  misunderstand  me 
here.  It  is  not  the  case  that  there  is  any  special  difficulty 
with  the  general  theory,  nor  any  apparent  discrepancy  be- 
tween theory  and  observation.  The  difficulty  that  I  speak 
of  is  purely  one  of  mathematical  analysis,  and  arises  en- 
tirely from  the  limitations  of  our  skill  in  that  branch  of 
art.  Doubtless  it  will  be  overcome  in  time. 

Meanwhile  we  are  constantly  reminded  that  "  Nature  is 
not  embarrassed  by  difficulties  of  analysis/'  and  that,  in 
our  interpretation  of  Nature,  we  must  not  allow  such 
difficulties  to  embarrass  us  unduly.  Thus,  in  the  present 
case,  although  a  rigorous  mathematical  solution  is  as  yet 
unattainable  in  general,  it  may  be  possible  to  get  an 
approximately  accurate  solution  which  is  good  enough  for 
practical  purposes.  As  a  matter  of  fact,  this  has  already 
been  done,  and  the  results  are  found  to  be  as  accurate  as 
we  need  in  the  present  state  of  our  experimental  skill. 
Thus  the  difficulties  of  mathematical  analysis  to  which 
reference  has  been  made  may  very  properly  be  handed 
over  to  our  successors,  whose  finer  instruments  and  more 
accurate  observations  may  demand  a  correspondingly  re- 
fined analysis.  The  method  that  is  generally  adopted  in 
dealing  with  such  problems  to-day  is  to  make  use  of  what 
is  known  as  the  Principle  of  Huyghens.  Let  us  look  once 
more  at  Fig.  62,  with  which  we  dealt  at  the  outset  of  this 
lecture.  A  disturbance  was  set  up  at  the  point  S,  and 
from  this  point  waves  traveled  out  in  all  directions.  If  this 


DIFFRACTION  209 

be  true  of  the  point  S,  we  should  expect  it  to  be  true  for 
any  other  point  that  is  disturbed;  whether  the  initial  dis- 
turbance be  set  up  by  a  stone  or  some  other  agent  can 
make  no  difference,  and  there  is  nothing  peculiar  to  S, 
except  that  it  happened  to  be  the  point  that  was  disturbed 
first.  Hence,  any  other  point,  such  as  P,  must  be  re- 
garded as  a  center  of  disturbance  from  which  waves  pro- 
ceed in  all  directions.  The  Principle  of  Huyghens  merely 
states  that  each  point  of  the  front  of  an  advancing  wave 
may  be  regarded  as  a  center  from  which  secondary  waves 
spread  out,  not  in  one  direction,  such  as  Pa,  but  in  all 
directions.  What  will  be  the  effect  of  the  combination  of 
all  the  secondary  waves  thus  set  out  is  a  question  to  be 
answered  by  the  help  of  the  Principle  of  Interference, 
which  makes  it  clear  that  the  effect  will  depend  on  the 
amplitudes  and  phases  of  the  various  secondary  waves 
that  have  to  be  considered.  To  determine  exactly  what 
is  the  law  governing  these  features  of  the  secondary  waves 
is  a  difficult  problem.  It  was  attacked  by  Stokes  in  a 
famous  memoir  "On  the  Dynamical  Theory  of  Diffraction." 
In  this  the  problem  was  to  determine  what  must  be  the 
amplitudes  and  phases  of  the  secondary  waves,  so  that  in 
combination  these  waves  would  give  the  actual  disturb- 
ance in  front  of  the  advancing  wave  and  no  disturbance  at 
all  behind  it.  Interesting  and  instructive  as  was  Stokes' s 
discussion  of  this  problem,  his  solution  has  not  escaped 
criticism.  Amongst  other  things  it  has  been  pointed  out 
that  the  problem  is  really  an  indeterminate  one.  The 
question  asked  is  one  that  can  have  several  answers,  like 
the  question,  What  two  integers,  when  added  together, 
make  6  ?  and  there  is  nothing  to  determine  which  of  the 
answers  is  to  be  preferred.  Various  laws  have  been  sug- 


210  LIGHT 

gested  other  than  the  one  that  Stokes  arrived  at,  and  it 
should  be  noted  that,  while  differing  in  other  respects, 
they  agree  as  to  the  disturbance  produced  by  the  secondary 
waves  in  the  only  region  where  these  waves  are  really 
effective,  i.e.  in  the  neighborhood  of  the  direction  PQ. 
The  waves  that  travel  in  all  other  directions  have  their 
influence  neutralized  through  interference  with  other 
waves.  If,  then,  we  wish  to  estimate  the  effect  of  all  the 
secondary  waves  that  pass  over  Q,  it  appears  that  we 
need  consider  those  only  that  set  out  from  the  wave-front 
OP  in  the  neighborhood  of  P.  It  is  for  this  reason  that  PQ 
is  sometimes  spoken  of  as  the  path  of  the  effective  disturb- 
ance that  passes  from  P  to  Q,  and  this  effective  disturbance 
constitutes  the  ray  of  light. 

Let  us  suppose,  now,  that  a  screen  OF  is  interposed  so  as 
to  interfere  with  the  advance  of  the  waves  in  the  ether. 
How  will  this  affect  the  propagation  of  the  waves  and 
the  optical  phenomena  in  the  region  beyond  the  screen? 
This  is  a  hard  question  to  answer,  owing,  as  has  been  ex- 
plained, to  the  mathematical  difficulties  that  arise  in  its 
discussion.  These  difficulties  have  been  completely  over- 
come only  in  one  or  two  special  cases,  but  an  approxi- 
mate solution  has  been  reached  in  many  others.  To  ob- 
tain this,  an  assumption  is  made  that  is  certainly  not 
justified  if  we  insist  on  absolute  rigor  and  exactness 
throughout.  Such  a  lofty  attitude,  however,  makes  prog- 
ress impossible,  and  as  practical  men  we  prefer  to  make 
some  advance,  even  by  means  of  an  unjustifiable  assump- 
tion, provided  we  have  reason  to  suppose  that  this  assump- 
tion will  not  lead  us  too  far  astray.  The  assumption 
made  is  that  the  effect  of  the  screen  is  merely  to  destroy 
the  secondary  waves  that,  but  for  its  presence,  would  be 


DIFFRACTION  211 

propagated  from  the  various  points  of  its  surface,  while 
all  the  other  secondary  waves  from  points  not  on  the 
screen  go  forward  just  as  if  the  screen  were  away.  It  is 
easy  to  see  that  this  cannot  be  quite  strictly  true.  Con- 
sider the  simple  case  of  a  stream  of  water  flowing  in  a 
closed  space  between  two  horizontal  boards  represented  in 
section  by  AB  and  CD  in  Fig.  63  a.  Each  particle  would 
move  horizontally,  along  lines  such  as  the  dotted  ones 


D 


(a)  (6) 

FIG.  63 

of  the  figure.  Now  put  in  an  obstacle,  such  as  OF  in 
Fig.  63  b.  This  would  do  more  than  merely  stop  the 
onward  rush  of  the  drops  of  water  that  struck  the  obstacle. 
It  would  affect  the  motion  in  the  neighborhood  of  F,  and 
the  motion  below  and  to  the  right  of  that  point  in  Fig. 
63  b  would  not  be  just  the  same  as  at  the  corresponding 
point  of  Fig.  63  a.  In  the  case  of  waves  it  appears, 
however,  on  investigation,  that  the  error  introduced  by 
this  assumption  is  inappreciable  except  within  a  few  wave- 
lengths of  the  edge  of  the  obstacle.  We  shall  see  before 
the  close  of  this  lecture  that  there  are  something  like 
50,000  wave-lengths  of  light  to  the  inch,  and  owing  to  this 
extreme  shortness,  the  region  of  error  due  to  the  false 
assumption  is  so  small  as  to  be  practically  negligible. 
Proceeding,  then,  with  this  assumption,  we  are  able  to  com- 
pute all  the  essential  details  of  the  optical  phenomena  in 
a  large  number  of  interesting  cases,  and  in  many  of  these 
to  test  our  (admittedly  imperfect)  theory  by  comparison 


212  LIGHT 

with  the  most  careful  measurements  that  are  available. 
This  was  first  done  by  Fresnel  in  a  classical  memoir  on 
Diffraction  that  was  crowned  by  the  French  Academy  in 
1819.  Fresnel  considered  the  case  of  light  falling  on  an 
opaque  screen  with  a  straight  edge.  If  the  light  were 
propagated  strictly  in  straight  lines,  there  would  be  a 
sharply  defined  shadow,  coinciding  with  the  geometrical 
shadow,  the  contour  of  which  is  determined  by  drawing 


FIG.  64 

straight  lines  from  the  source  of  light  to  the  edge  of  the 
screen.  Inside  this  shadow  there  would  be  absolute  dark- 
ness, and  outside  it  uniform  brightness.  The  curve  of  in- 
tensity would  then  be  the  dotted  curve  of  Fig.  64.  In 
this  0  represents  the  position  of  the  edge  of  the  geometrical 
shadow,  the  shadow  being  to  the  left  of  0.  OP  represents 
the  intensity  of  the  incident  light,  as  well  as  that  in  the 
bright  part  of  the  field  at  some  distance  from  the  edge  of 
the  shadow.  Fresnel  showed  that  the  theory  that  has 
just  been  sketched  would  lead  us  to  expect  a  distribution 
of  light  that  is  indicated  by  the  continuous  line  of  the 
figure  (abode...).  It  will  be  observed  that  there  is  no 
longer  complete  darkness  to  the  left  of  0,  but  that  the  light 
fades  away  rapidly  as  we  go  into  the  shadow.  Perhaps 
the  most  striking  result  of  the  investigation  is  that  outside 
the  shadow  (to  the  right  of  0  in  the  figure)  the  intensity  of 


DIFFRACTION 


213 


the  light  is  not  uniform,  but  that  there  are  a  series  of 
bright  bands  where  the  intensity  is  much  greater  than  the 
average  (c,  e,  #...),  alternating  with  bands  where  it  is 
much  less  (d,  /,  h...).  The  theory  indicates,  and  this 
is  fully  confirmed  by  experience,  that  the  exact  distribution 
of  light  depends  on  the  wave-length  of  the  incident  beam. 
Fresnel  calculated  the  details  for  red  light  of  wave-length 
0.000638  millimeters  or  0.000025  inches.  The  intensity  of 
the  light  at  the  brightest  bands,  corresponding  to  c,  e,  g... 
of  Fig.  64,  when  expressed  in  percentage  of  the  intensity  of 
the  incident  light,  was  found  to  be  137,  120,  115,  113,  111, 
110,  109...,  and  that  at  the  intermediate  darks  bands 
(d,  f,  h...)  to  be  78,  84,  87,  89,  90,  91,  92...  Owing 
to  the  difficulty  of  making  very  accurate  measure- 
ments of  intensity,  it  was  not  easy  to  make  a  searching 
test  of  the  theory  by  comparing  these  results  with  those 
derived  from  experiment.  There  is,  however,  another  fea- 
ture that  is  more  easily  measured  with  accuracy,  and  that 
is  the  distances  of  the  different  fringes  from  the  edge  of  the 
geometrical  shadow.  The  following  table  gives  the  posi- 
tions, obtained  from  theory  and  also  from  observation,  of 
the  first  five  dark  bands  for  the  red  light  used  by  Fresnel. 
The  results  are  set  out  for  three  different  distances  (d)  of 


ct=100 

d  =  1011 

d=6007 

Theory 

Observation 

Theory 

Observation 

Theory 

Observation 

First  Fringe   .     . 

2.83 

2.84 

2.59 

2.59 

1.14 

1.13 

Second  Fringe     . 

4.14 

4.14 

3.79 

3.79 

1.67 

1.67 

Third  Fringe.     . 

5.13 

5.14 

4.69 

4.68 

2.07 

2.06 

Fourth  Fringe     . 

5.96 

5.96 

5.45 

5.45 

2.40 

2.40 

Fifth  Fringe  .     . 

6.68 

6.68 

6.11 

6.10 

2.69 

2.69 

214  LIGHT 

the  screen  from  the  source  of  light.  All  the  distances  are 
given  in  millimeters,  and  you  will  remember  that  one  milli- 
meter is  equal  to  0.03937  inches.  It  will  be  seen  that  the 
agreement  between  theory  and  observation  is  excellent. 
The  position  of  the  bright  bands  depends  upon  the  wave- 
length, and  so  on  the  color  of  the  light.  If,  then,  we  em- 
ploy a  mixture  of  colors  such  as  constitute  white  light,  we 
shall  get  a  series  of  colored  fringes  in  slightly  different  posi- 
tions. These  will  tend  to  overlap  one  another,  and  the 
overlapping  will  make  it  difficult  to  distinguish  the  outer 
bands  of  color.  Hence,  for  accurate  measurements  designed 
to  test  any  theory,  it  is  expedient  to  use  homogeneous  light, 
and  so  have  only  a  single  wave-length  to  deal  with. 

The  same  general  method  will  enable  us  to  discuss  the 
phenomena  to  be  looked  for  in  various  other  circum- 
stances. Thus,  instead  of  dealing  with  a  single  straight 
edge,  we  may  wish  to  examine  the  effect  of  two  parallel 
edges  close  together  constituting  a  narrow  slit.  The  simplest 
apparatus  to  use  for  such  experimental  purposes  is  your 
own  hand.  Hold  two  fingers  together  so  that  they  are 
very  nearly  closed,  and  look  through  the  narrow  opening 
at  a  distant  bright  object.  You  will  see  a  number  of 
colored  fringes,  but  if  you  wish  to  investigate  the  phe- 
nomena carefully,  it  will  be  better  to  take  a  little  more 
trouble  and  proceed  as  follows.  Cut  a  slit  about  an 
eighth  of  an  inch  wide  in  a  black  card  and  fix  this  in  front 
of  a  bright  light.  Look  at  this  slit  through  the  narrower 
slit  made  by  drawing  with  the  point  of  a  needle  a  straight 
line  on  a  piece  of  blackened  glass,  and  hold  the  two  slits 
parallel  to  one  another.  You  will  at  once  observe  a  series 
of  colored  spectra.  If  you  make  the  light  homogeneous  by 
interposing,  say,  a  red  glass  between  the  light  and  the 


DIFFRACTION 


215 


first  slit,  you  will  see  a  series  of  bright  red  bands,  R1  R%... 
(Fig.  65),  on  each  side  of  the  central  image  R,  and  you 
will  notice  that  their  intensity  diminishes  as  you  get 
further  away  from  the  central  band.  On  replacing  the 
red  by  blue,  you  will  observe  a  similar  effect,  but  the  bright 
blue  bands  will  be  narrower  and  closer  together  than  were 
the  red,  as  is  indicated  roughly  in  the  figure  by  the  posi- 
tions of  the  rectangles  B,  Bv..  You  see  from  this  that 
if  both  colors  are  present  together,  the  different  bands  will 
overlap,  and  you  will  understand  the  various  spectra  that 


R 

^  PI  p 

R 

R3 

*i 

R 

*, 

R2 

FIG.  65 

are  seen  when  white  light  is  employed.  By  fixing  a  nar- 
row slit  on  the  end  of  your  opera  glasses,  you  can  readily 
see  these  spectra  and  examine  their  details  at  your  leisure. 
Closely  allied  to  the  case  of  a  narrow  slit  is  that  of  a 
narrow  obstacle  placed  in  the  path  of  a  beam  of  light. 
Reference  has  already  been  made  to  Newton's  experiment 
with  a  human  hair,  which  exhibits  the  phenomena.  You 
can  easily  see  this  for  yourselves  by  partially  closing  your 
eyes  and  looking  at  a  bright  light  through  your  eyelashes. 
A  fine  wire  is  now  placed  in  front  of  the  lantern,  and  you 
observe  that  the  dark  shadow  on  the  screen  is  bordered 
with  colored  fringes,  and  now  that  a  mesh  of  wires  is  sub- 
stituted for  the  single  wire,  you  see  that  the  color  effects 
are  quite  gorgeous.  The  effects  to  be  expected  from 
apertures  and  obstacles  of  various  forms  have  been  care- 
fully examined  both  theoretically  and  experimentally,  and 


216  LIGHT 

the  agreement  between  theory  and  observation  is,  on  all 
points,  most  satisfactory.  We  have  time  only  to  select  a 
single  example,  that  of  a  circular  aperture  (and  the  cor- 
responding case  of  a  circular  obstacle).  This  is  especially 
important,  owing  to  the  fact  that  most  optical  instruments 
(telescopes,  microscopes,  and  the  like)  are  arranged  so  that 
the  light  passes  into  them  through  a  circular  aperture. 
The  mathematical  analysis  of  the  case  is  long  and  some- 
what complex,  but  the  fundamental  principles  employed 
are  the  same  as  those  that  have  already  been  explained. 
The  investigation  shows  that  where  light  shines  through  a 
circular  aperture  upon  a  screen,  the  screen  is  not  uni- 
formly illuminated,  but  that  there  are  marked  variations 
in  the  intensity  at  different  portions  of  the  circular  patch 
of  light.  The  points  where  the  brightness  is  least  con- 
stitute a  series  of  concentric  dark  rings  whose  radii  can 
be  determined  from  theory,  and,  of  course,  observed  ex- 
perimentally. The  sizes  of  these  rings  depend  on  the 
color  of  the  light,  so  that  when  white  light  is  employed, 
the  screen  exhibits  a  series  of  colored  rings.  Lommel 
made  careful  determinations  of  the  radii  of  these  rings 
for  various  colors,  and  compared  his  observations  with  the 
deductions  from  theory.  The  results  for  the  first  four 
dark  rings  are  set  out  in  the  table  below  for  a  few  cases, 
but  Lommel  dealt  with  over  180  such  cases,  and  in  all  of 
these  the  agreement  between  theory  and  observation  was 
as  good  as  in  those  here  selected.  The  different  colors 
used  were  red,  orange,  green,  and  blue,  corresponding  to 
the  spectral  lines  known  as  C,  D,  E,  and  F  and  to  wave- 
lengths of  0.0006562,  0.0005889,  0.0005269,  and  0.0004861 
millimeters.  The  radius  of  the  aperture  was  0.28,  the 
distance  of  the  edge  of  the  aperture  from  the  source  of 


DIFFRACTION 


217 


light  was  2120,  and  of  the  source  of  light  from  the  screen, 
2210.4.  These  numbers  and  those  in  the  table  all  repre- 
sent millimeters. 


BLUB 

GREEN 

ORANGE 

RED 

Theory 

Observation 

Theory 

Observation 

Theory 

Observation 

Theory 

Observation 

0.015 



0.032 

0.034 

0.057 

0.056 

0.082 

0.082 

0.156 

0.158 

0.179 

0.175 

0.308 

0.305 

0.237 

0.231 

0.254 

0.254 

0.275 

0.276 

0.403 

0.406 

0.343 

0.338 

0.333 

0.333 

0.361 

0.361 





0.449 

0.451 

Theory  also  enables  us  to  calculate  the  intensity  of  the 
light  at  different  positions  on  the  screen.  It  thus  appears 
that  about  84  per  cent  of  the  whole  light  is  inside  the  first 
dark  ring.  The  central  spot  is  not,  however,  of  uniform 
brightness,  but  shades  off  as  we  proceed  outwards  from 
the  center,  the  intensity  halfway  between  the  center  and 
the  first  dark  ring  being  about  37  per  cent  of  that  at  the 
center.  Perhaps  the  most  important  result  to  bear  in 


FIG.  66 


mind  is  that  the  image  of  a  point  is  not  a  point,  but  a 
complicated  system  of  rings  of  the  kind  indicated  roughly 
in  Fig.  66  a.  Figure  66  b  represents  the  image  of  two 
points  close  together,  and  shows  how  the  two  images  tend 


218 


LIGHT 


to  overlap  and  produce  a  blurred  effect.  Fortunately,  most 
of  the  light  is  confined  within  the  first  ring,  so  that  we  do 
not  go  far  wrong  in  supposing  that  the  image  of  a  point 
as  seen  through  a  telescope  is  a  small  disk.  Do  what  we 
will,  however,  we  cannot  make  this  disk  shrink  to  a  point, 
and  when  we  take  a  photograph  we  set  the  light  the  diffi- 
cult problem  of  drawing  a  clear  picture  with  a  blunt 
pencil.  The  bluntness  of  the  pencil  depends  upon  the 
diameter  of  the  little  disk  of  light,  and  to  sharpen  it  as 
much  as  possible  we  must  increase  the  size  of  the  aper- 
ture and  use  light  of  the  shortest  wave-length  that  can 
be  employed.  Fortunately,  for  photography,  the  short 
waves  have  great  actinic  power;  but  the  other  require- 
ment, that  of  a  large  aperture,  is  not  so  easily  satisfied 
and,  as  it  involves  great  size,  adds  seriously  to  the  cost  of 
the  best  telescopes  used  for  astronomical  purposes. 

The  corresponding  problem  presented  by  the  shadow  of 
an  opaque  disk  was  also  solved  by  Lommel.  Here,  too, 
we  have  a  series  of  alternations  of  light  and  darkness,  giving 
the  appearance  of  a  number  of  concentric  rings  with  their 
center  at  the  center  of  the  shadow.  The  table  below  gives 
the  radii  of  the  first  four  dark  rings  in  a  few  cases;  but 
Lommel  dealt  with  over  sixty  cases  in  all,  and  found  the 
same  good  agreement  between  theory  and  observation. 


BLUE 

GREEN 

ORANGE 

BED 

Theory 

Observation 

Theory 

Observation 

Theory 

Observation 

Theory 

Observation 

0.088 

0.090 

0.096 

0.096 

0.109 

0.113 

0.119 

0.124 

0.200 

0.197 

0.219 

0.220 

0.242 

0.237 

0.268 

0.265 

0.307 

0.310 

0.335 

0.333 

0.369 

0.367 

0.403 

0.400 

0.406 

0.406 

0.438 

0.440 

0.478 

0.479 

0.525 

0.525 

•*     OF  THE 


UNIV 

DIFFRACTION  219 


i^C> 


Here  the  radius  of  the  disk  was  0.32,  and  the  distance  of 
its  edge  from  the  source  of  light  was  1485.  Observations 
were  made  with  the  four  colors  previously  mentioned,  — 
blue,  green,  orange,  and  red,  —  the  distance  of  the  screen 
from  the  source  of  light  being  1639.9,  1642.6,  1643.3,  and 
1643.2  for  the  different  colors.  All  the  numbers  represent 
millimeters.  The  different  radii  for  the  different  colors 
give  an  idea  of  the  amount  of  overlapping  when  white 
light  is  employed,  and  of  the  arrangement  of  the  colors  in 
the  fringes.  In  this  case  also  theory  enables  us  to  calcu- 
late the  intensity  of  the  light  at  different  points  in  the 
shadow.  In  this  connection  one  feature  may  be  pointed 
out,  as  it  is  probably  unexpected.  It  appears  from  the 
investigation  that  at  the  very  center  of  the  shadow  there 
should  be  a  bright  spot,  and  that  this  should  be  just  as 
bright  as  if  there  were  no  disk  present  to  cut  off  the  light. 
This  deduction  seemed  so  absurd  when  it  was  first  an- 
nounced that  it  was  regarded  as  a  serious  objection  to  the 
wave  theory.  A  little  care,  however,  in  experiment  showed 
nevertheless  that,  however  unexpected  or  seemingly  im- 
possible, it  was  none  the  less  perfectly  true.  If  you  have 
the  resources  of  a  physical  laboratory  at  your  disposal, 
you  will  find  no  great  difficulty  in  trying  this  for  yourself. 
You  will  need  a  carefully  made  circular  disk  that  is  not 
too  large,  and  you  will  need  to  make  the  necessary  adjust- 
ments with  some  precision.  I  will  modify  the  experiment 
so  as  to  exhibit  the  result  to  the  whole  audience  and  deal 
with  sound-waves  rather  than  with  light,  so  as  to  work 
on  a  larger  scale.  The  mathematical  analysis  is  very 
similar  in  the  two  cases,  but  the  sound-waves  have  the 
advantage  of  being  much  longer,  so  that  we  do  not  need 
the  same  refinement.  Introducing  you  once  more  to  this 


220  LIGHT 

whistle  and  sensitive  flame,  I  fix  a  circular  disk  of  glass, 
about  a  foot  in  diameter,  between  the  two.  By  moving 
the  whistle  into  different  places,  you  observe  that  there  is 
a  marked  sound  shadow  behind  the  disk;  but  now  that, 
after  some  adjustment,  I  have  got  the  whistle  so  that  it 
is  exactly  opposite  the  center  of  the  disk,  you  see  that 
the  flame  ducks,  and  by  doing  so  indicates  the  presence  of 
a  considerable  disturbance  in  the  air. 

The  applications  of  the  theory  of  diffraction  to  the 
construction  of  optical  instruments  and  to  the  explanation 
of  various  optical  phenomena  are  so  numerous  that  it 
would  be  impossible  in  the  time  at  our  disposal  to  deal 
with  them  at  all  adequately.  In  the  short  time  that  re- 
mains to  me  for  this  lecture  I  shall  endeavor  to  explain 
very  briefly  how  it  is  that  the  principles  of  diffraction 
enable  us  to  measure  the  lengths  of  different  waves  of 
light  and  to  measure  them  with  wonderful  accuracy. 
Several  methods  may  be  employed  for  this  end,  but  I 
shall  confine  myself  to  what  is  the  simplest  for  purposes 
of  exposition.  This  measures  the  wave-lengths  by  the 
aid  of  a  diffraction  grating,  an  extremely  simple  instrument 
as  far  as  its  appearance  is  concerned.  It  is  made  by  rul- 
ing a  great  number  of  very  fine  parallel  lines  on  speculum 
metal  or  glass.  The  former  is  viewed  by  reflection,  as  the 
metal  reflects  a  large  proportion  of  the  incident  light,  and 
is  called  a  reflection  grating.  The  glass  reflects  some  light, 
and  usually  transmits  more.  If  viewed  by  transmission, 
i.e.  if  the  incident  light  be  allowed  to  stream  through  the 
grating  and  the  transmitted  beam  be  then  examined,  the 
arrangement  is  described  as  a  transmission  grating.  In 
either  of  these  cases  the  effect  of  the  grooves  made  by 
ruling  is  to  scatter  irregularly  the  light  that  falls  on  them, 


DIFFRACTION 


221 


so  that  the  grooves  behave  as  if  they  were  opaque  and 
destroyed  the  light  that  strikes  them.  Let  us  consider 
light  falling  normally  on  a  transmission  grating,  a  cross- 
section  of  the  surface  of  which  is  represented  in  Fig.  67. 
The  thick  lines  in  this  figure,  such  as  x^,  z2a3...,  show 
the  positions  of  the  grooves,  which,  as  we  have  just  seen, 


FIG.  67 

practically  stop  all  the  light  that  falls  on  them.  Waves 
enter  the  instrument  through  the  portions  a-^x^  a%x2...,  and 
if  we  consider  a^  as  the  front  of  an  entering  wave,  then 
every  point  on  this  front  is  to  be  regarded  (as  was  stated 
earlier)  as  a  center  of  disturbance  from  which  waves,  and 
therefore  rays,  spread  out  in  all  directions.  If  the  front 
of  the  incident  wave  were  complete,  that  is,  if  there  were 
no  obstructing  grooves,  the  waves  that  spread  out  laterally 
in  any  such  direction  as  a^  would  be  nullified  by  inter- 
ference with  the  waves  that  proceed  from  other  portions 
of  the  wave-front,  and  it  would  only  be  directly  in  front 
of  «!  that  the  effective  disturbance  would  be  appreciable. 
The  grooves,  however,  cut  out  some  of  the  waves  that 


222  LIGHT 

would  contribute  to  this  interference.  This  must  modify 
the  results,  so  that  it  may  well  be  that  there  is  an  ap- 
preciable disturbance  in  some  such  direction  as  a^. 

To  investigate  this  matter  more  fully,  we  must  bear  in 
mind  the  fundamental  idea  that  lies  at  the  root  of  the 
Principle  of  Interference;  namely,  that  two  waves  that 
are  similar  in  all  other  respects,  but  that  differ  in  phase 
by  half  a  wave-length,  or  any  odd  multiple  thereof,  will 
interfere  and  produce  darkness,  while  if  they  differ  in 
phase  by  a  whole  wave-length,  or  any  multiple  thereof, 
they  reinforce  one  another  and  give  greater  intensity  of 
light.  Let  us  consider  all  the  secondary  waves  that  travel 
outward  from  the  various  points  of  the  incident  wave- 
front  in  a  given  direction,  such  as  a^  (to  which  azn2  and 
a3n3  in  the  figure  are  parallel).  The  difference  of  phase 
between  the  waves  from  al  and  a2  is  represented  by  a^', 
where  a^  is  perpendicular  to  a^n^  This  will  also  be 
equal  to  the  difference  of  phase  between  the  waves  from 
&!  and  &2,  provided  a262  be  equal  to  ajb^  Now  if  the  grooves 
be  of  exactly  the  same  width,  and  the  spaces  between  them  be 
equal,  it  will  be  possible  to  divide  all  the  spaces  into  the 
same  number  of  equal  parts,  so  that  a1&1  =  61c1  =  ...  =  a262  = 
&2c2  =  ...=a3&3  =  &3c3  =  ....  We  shall  also  have  a1n1  =  a2n2  = 
a3n3  =  ...,  and  the  difference  of  phase  between  the  secondary 
waves  from  al  and  a2  will  be  the  same  as  between  those  from 
&!  and  62  or  from  cl  and  c2,  or  from  a2  and  a3  or  from  62  and  b3, 
and  so  on.  Let  us  suppose,  further,  that  the  incident  light 
is  homogeneous,  i.e.  all  of  the  same  wave-length,  and  that 
a^i  is  half  this  length.  Then  if  all  the  secondary  waves 
could  be  brought  together  without  relative  change  of 
phase,  the  wave  from  a1  would  interfere  with  that  from  a2, 
the  wave  from  6j  would  interfere  with  that  from  62;  and 


DIFFRACTION  223 


so  on,  thus  producing  darkness  in  the  direction 
The  combination  of  the  different  secondary  waves 
is  simply  effected  by  means  of  a  lens,  which  bends 
the  rays  so  as  to  bring  them  to  a  focus,  and  alters  the 
direction  of  the  wave-motion  without  changing  the  rela- 
tive phase  of  the  different  waves.  Let,  then,  OA  in  Fig.  68 
represent  one  of  the  lines  in  the  grating,  and  OB  a  line 
drawn  at  right  angles  to 
the  plane  of  the  grating 
to  meet  a  screen,  on  which 
the  light  falls,  at  B.  If 
OD1  be  drawn  in  the  di- 
rection represented  by 
a^  in  Fig.  67,  and  DjZy 
be  drawn  on  the  screen 
parallel  to  OA,  then  from 
what  has  been  said  it  will 
be  seen  that  Di/Y  will  coincide  with  a  dark  line  on  the 
screen.  This,  however,  will  not  be  the  only  dark  line, 
for  the  same  interference  will  take  place  when  a-pii  is 
equal  to  any  odd  multiple  of  half  a  wave-length  as  when 
it  is  simply  half  a  wave-length.  If  OZ)2,  OZ)8,...  be 
the  directions  corresponding  to  phase  difference  of  three 
half  wave-lengths,  five  half  wave-lengths,  and  so  on,  then 
there  will  be  dark  lines  D2D2',  D3D3',...,  all  parallel 
to  OA.  We  have  dealt  with  the  case  where  a^  is  half 
a  wave-length  or  any  odd  multiple  thereof.  Let  us  sup- 
pose next  that  a^  is  a  wave-length,  or  any  exact  number 
of  wave-lengths.  Then  the  various  secondary  waves,  in- 
stead of  interfering,  will  reinforce  one  another,  and  the 
corresponding  portions  of  the  field  will  be  unusually 
bright.  We  shall  thus  have  a  series  of  bright  lines,  such 


224  LIGHT 

as  #!#/,  #2ZY>-->  m  Fig.  68.  On  comparing  the  triangle 
a^aj  of  Fig.  67  with  OBBl  of  Fig.  68,  it  is  seen  that  these 
triangles  have  equal  angles.  The  angle  a^n^  is  equal  to 
the  angle  OBBl}  as  each  is  a  right  angle,  and  the  angle 
n^aj  is  equal  to  the  angle  BOBV  since  OB  is  perpendicular 
to  tt^,  and  OBl  is  parallel  to  a^n^  and  therefore  perpendicu- 
lar to  n^.  As  the  two  triangles  have  equal  angles,  it 
follows  geometrically  that  they  must  be  similar  triangles 
differing  only  in  scale.  Hence  the  ratio  of  a^  to  axa2 
must  be  equal  to  the  ratio  of  BBl  to  OBlt  or,  in  algebraic 

symbols,  ^1  =  -—  1.   Thus  we  have  a^  =  a^  x  •—  1.  Now 


. 
On1 

can  be  measured  accurately  by  counting  the  number 
of  grooves  in  a  given  distance.  Thus,  if  on  the  grating 
there  are  twenty  thousand  lines  to  the  inch  (there  are 
more  than  this  on  many  good  gratings),  then  a^  is  one 
twenty-thousandth  of  an  inch.  The  distances  BB1  and 
OB1  might  be  measured  directly,  but  it  is  only  their  ratio 
that  is  wanted,  and  this  can  be  determined  most  simply 
and  accurately  by  the  aid  of  trigonometry,  once  the  angle 
BOBl  has  been  measured.  The  measurement  of  this 
angle  can  be  made  with  great  precision  and  then,  from 

T>T> 

the  equation  ohtti  =  a^  x  —  —  J  =  a^  sin  BOBl}  the  quantity 


is  readily  calculated.  It  has  been  indicated,  however, 
that  this  quantity  a^  is  the  wave-length  of  the  light 
with  which  we  are  dealing,  so  that  the  problem  of  deter- 
mining the  wave-length  has  been  solved. 

If  the  process  thus  sketched  be  carried  out  carefully 
with  a  good  grating,  the  wave-lengths  may  be  determined 
with  marvellous  accuracy.  There  are  several  ways  of 
testing  the  results.  Thus,  if  we  deal  with  the  bright  line 


DIFFRACTION  225 


B^BI,  the  calculated  value  of  a^  should  be  the  wave- 
length. If  we  make  similar  measurements  with  B^B^, 
then  the  corresponding  value  of  a^  should  be  twice  the 
wave-length;  with  BBBB'  it  should  be  thrice  this  length, 
and  so  on.  The  consistency  of  the  various  estimates  of 
the  wave-length  thus  obtained  will  enable  us  to  form  an 
estimate  of  the  accuracy  of  our  results.  Then,  too,  we 
need  not  confine  our  attention  to  the  case  of  light  that 
strikes  the  grating  at  right  angles  to  its  surface.  This  case 
has  been  dealt  with  and  illustrated  in  order  to  simplify 
the  mathematical  discussion  as  much  as  possible;  but  it 
requires  a  very  slight  effort  to  extend  the  argument  to  the 
more  general  case  of  oblique  incidence  and  to  obtain  a 
corresponding  formula  for  the  wave-length.  By  making 
observations  at  various  angles  of  incidence  and  computing 
the  wave-length,  we  have  other  means  of  testing  the  con- 
sistency and  accuracy  of  our  results,  and  when  all  pre- 
cautions are  taken,  it  is  found  that  these  results  are 
marvellously  concordant.  For  this  end,  of  course,  a  good 
grating  is  indispensable,  and  a  good  grating  is  an  instru- 
ment that  requires  great  care  and  skill  in  the  making. 
The  rulings  must  be  made  with  almost  perfect  accuracy, 
for  the  argument  supposes  that  the  distance  between  the 
various  grooves  and  their  width  is  uniform  throughout, 
and  if  this  be  not  the  case  errors  will  inevitably  creep  in. 

There  are  other  methods  of  measuring  wave-lengths 
than  the  one  here  described,  but  time  will  not  permit  us 
to  discuss  them.  Suffice  it  to  say  that  few  things  can 
now  be  measured  with  such  wonderful  precision  as  the 
length  of  a  wave  of  light.  Such  is  the  accuracy  that  has 
been  attained,  that  it  has  been  seriously  proposed  that 
the  length  of  a  wave  of  light  emitted  under  certain  condi- 
Q 


226  LIGHT 

tions  from  a  specified  substance  should  be  adopted  as  the 
standard  of  length.  This  standard  would  have  some  ad- 
vantages over  any  that  are  now  in  use,  for  all  these  are 
subject  to  slow  and  uncertain  changes,  and  the  one  thing 
to  be  required  of  a  standard  above  all  else  is  that  it  should 
not  change.  The  length  of  a  wave  of  light  emitted  by  a 
substance  depends  on  properties  of  the  ether  and  of  the 
atom  that,  there  is  reason  to  believe,  are  invariable,  so  that 
this  length  seems  capable  of  serving  as  a  true  standard. 
With  this  end  in  view  Michelson  devoted  himself  for  some 
time  to  the  problem  of  determining  the  length  of  the 
standard  meter  in  wave-lengths.  For  this  purpose  he  em- 
ployed certain  radiations  from  cadmium,  which  were 
chosen  on  account  of  their  simple  character.  He  found 
that  the  number  of  light-waves  in  the  standard  meter  in 
air  at  15°  C  and  normal  pressure  was  1,553,163.5  for  the 
red  waves  from  cadmium,  1,966,249.7  for  the  green,  and 
2,083,372.1  for  the  blue,  and  that  the  measurements  could 
be  made  so  accurately  that  he  could  safely  say  that  the 
errors  were  less  than  one  part  in  two  millions. 

The  following  table  gives  some  details  with  reference  to 
wave-lengths  and  frequencies  of  the  waves  corresponding 
to  different  parts  of  the  spectrum.  The  letters  ABC... 
are  the  names  by  which  these  lines  in  the  solar  spec- 
trum are  known,  and  an  indication  of  their  color  is  given. 
The  wave-lengths  are  expressed  in  millionths  of  a  meter, 
and  the  frequencies  in  million  millions  per  second. 


DIFFRACTION 


227 


LINE  OF  SPECTRUM 

WAVE-LENGTH  IN 

MlLLIONTHS  OF  A 

METER 

NUMBER  OF  WAVES 

TO  THE   INCH 

FREQUENCY  IN 
MILLION  MILLIONS 
PER  SECOND 

A 

0.75941 

33,447 

395 

B 

0.68G75 

36,986 

437 

C  (red) 

0.65630 

38,702 

457 

D  (orange) 

0.58930 

43,102 

509 

E  (green) 

0.52697 

48,200 

569 

F  (blue) 

0.48615 

52,247 

617 

G  (violet) 

0.43080 

58,960 

696 

H 

0.39715 

63,956 

755 

Before  closing  this  lecture  there  is  one  feature  of  the 
phenomena  observed  when  using  a  grating  that  must 
not  be  overlooked.  We  have  seen  that  the  position  of 
the  bright  lines,  such  as  B-JZi,  depends  upon  the  length  of 
the  wave  employed.  It  follows  that,  if  the  incident  light 
be  white,  the  bright  lines  corresponding  to  its  various 
colored  constituents  will  have  different  positions,  so  that 
instead  of  a  single  bright  white  line  at  BiBi,  there  will  be 
a  whole  series  of  such  lines  forming  a  continuous  spectrum, 
with  all  the  colors  of  the  rainbow,  in  the  neighborhood  of 
#!#/.  There  will  be  a  similar  spectrum  near  J22-B2',  and 
so  for  the  other  lines,  and  to  distinguish  these  various 
spectra  from  one  another  they  are  spoken  of  as  spectra  of 
the  first  order,  second  order,  or  third  order,  and  so  on,  as 
the  case  may  be.  It  was  mentioned  in  the  lecture  on 
Spectroscopy  that  a  prism  was  not  the  only  means  of 
producing  dispersion  and  obtaining  a  spectrum,  and  we 
see  now  how  this  can  be  done  by  means  of  a  diffraction 
grating.  The  spectrum  produced  by  a  grating  has  one 
great  advantage  over  that  formed  by  a  prism  in  that  the 
distances  of  the  various  colored  lines  from  a  certain  fixed 


228  LIGHT 

line  are  proportional  to  the  wave-lengths,  as  the  above 
investigation  shows.  There  are  other  advantages  that 
cannot  now  be  discussed,  but  we  may  say  that  for  many 
purposes  of  accurate  measurement,  where  a  spectrum  is 
involved,  it  is  better  to  produce  this  spectrum  by  diffrac- 
tion rather  than  by  means  of  a  prism. 


X 

I 
LIGHT   AND   ELECTRICITY 

SCIENCE  has  a  vaulting  ambition.  It  views  the  whole 
field  of  human  knowledge  and  strives  to  possess  it  all. 
It  sets  about  this  tremendous  task,  however,  in  a  business- 
like way  and  recognizes  clearly  that,  for  practical  effec- 
tiveness, the  beginning  of  wisdom  is  limitation.  To  at- 
tempt too  much  is  to  court  failure,  and,  to  avoid  this, 
barriers  have  been  placed  across  the  field  of  knowledge, 
and  individuals  are  advised  to  work  strenuously  within  a 
little  fenced-in  portion  of  the  whole  field.  It  is  well,  how- 
ever, occasionally  to  reflect  that  all  the  fences  are  artificial, 
and  that  they  have  been  put  up  for  practical  purposes  and 
for  reasons  that  may  not  appeal  to  the  more  mature  judg- 
ment of  later  generations.  It  is  natural  and  convenient 
to  fence  off  from  one  another  things  that  seem  to  have 
little  or  nothing  in  common,  but  a  deeper  insight  may 
reveal  the  fact  that  there  is  the  closest  relationship  be- 
tween what  are  apparently  quite  different  things.  The  great 
divisions  of  natural  science  into  Physics,  Chemistry,  and 
Biology  are  proving,  after  all,  to  be  entirely  artificial,  and 
barriers  between  them  are  being  broken  down  almost 
daily.  And  if  this  be  true  of  the  great  divisions,  it  is  true 
even  more  obviously  of  the  subdivisions.  In  some  cases 
it  is  difficult  to  find  any  traces  to-day  of  barriers  that  in 
earlier  ages  seemed  natural  and  inevitable.  Thus,  in  one 
field  you  had  to  deal  with  what  affects  the  ear  and  goes 
by  the  name  of  sound;  in  another  your  problem  was  to 

229 


230  LIGHT 

discuss  the  mechanical  properties  of  gases  and  the  laws  of 
motion  within  them.  In  the  field  of  sound  you  learned 
to  distinguish  one  sound  from  another  by  its  intensity, 
by  its  pitch,  and  by  its  quality,  and  in  process  of  time  you 
established  various  laws  of  sound  that  enabled  you  to 
foretell  the  intensity,  pitch,  and  quality  of  sounds  emitted 
under  various  conditions.  In  the  other  field  you  found 
that  waves  could  be  set  up  in  gases,  and  that  these  could 
be  distinguished  by  their  amplitude,  by  their  frequency, 
and  by  their  form,  and  you  learned,  by  the  aid  of  me*- 
chanical  principles,  to  calculate  the  amplitude,  frequency, 
and  form  of  the  waves  set  up  in  given  circumstances.  In 
time  it  seemed  expedient  to  knock  down  the  fence  be- 
tween the  fields,  for  by  postulating  a  relation  between  the 
intensity  and  the  amplitude,  the  pitch  and  the  frequency, 
the  quality  and  the  form,  it  was  possible  to  explain  all  the 
peculiarities  of  sound  on  mechanical  principles,  and  to 
test  the  theory  by  experiment  in  the  most  rigorous  fashion 
that  could  be  demanded.  Thus  to-day  the  problem  of 
sound  is  regarded  as  a  small  part  of  the  wider  subject  of 
vibrations  (in  air  and  other  media),  the  vibrations  being 
confined  to  narrow  limits  determined  by  the  structure  of 
the  ear. 

No  two  physical  sciences  seem,  at  first  sight,  more 
widely  separated  than  light  and  electricity.  My  aim  in 
this  lecture  is  to  show  that  they  are  in  reality  most  in- 
timately related.  To  this  end  let  me  begin  by  reminding 
you  of  the  broadest  outlines  of  the  theory  of  light.  We 
have  seen  that  in  order  to  coordinate  the  great  mass  of 
phenomena  that  have  been  observed  in  the  field  of  optics, 
it  is  necessary  to  postulate  the  existence  of  a  medium 
that  we  call  the  ether,  and  that  we  endow  with  definite 


LIGHT  AND  ELECTRICITY  231 

and  peculiar  properties.  This  ether  is  capable  of  trans- 
mitting disturbances  by  means  of  waves  that  travel  through 
it  with  a  speed  that  is  determined  by  the  properties  of  the 
ether,  but  that  have  frequencies  depending  entirely  on  the 
source  of  the  disturbance.  If  the  frequency  be  within  cer- 
tain limits  that  are  determined  not  by  the  source  of  the  dis- 
turbance but  by  the  structure  of  the  eye,  the  waves  will 
produce  the  sensation  of  light.  If,  however,  the  frequency 
be  higher  than  the  limit  set  by  the  eye,  then  no  light  is 
seen;  but  the  waves  may  show  their  presence  in  other 
ways,  e.g.  by  their  influence  on  a  sensitive  photographic 
plate.  On  the  other  hand,  if  the  frequency  be  somewhat 
lower  than  this  limit,  the  waves  will  produce  the  sensation 
of  radiant  heat,  and  if  it  be  very  much  lower,  they  will  give 
rise  to  electrical  phenomena.  Thus,  from  this  point  of  view, 
the  distinction  between  photographic  action,  light,  radiant 
heat,  and  electricity  is  mainly  a  question  of  frequency,  and 
light  is  seen  to  be  only  a  small  portion  of  the  problem 
presented  by  the  propagation  of  waves  in  the  ether. 

As  a  matter  of  history  the  science  of  electricity  was 
built  up  quite  independently  of  that  of  light.  It  soon 
appeared  that  to  account  satisfactorily  for  electrical  phe- 
nomena it  was  necessary  to  postulate  the  existence  of  an 
ethereal  medium,  and  in  the  process  of  time  it  became 
evident  that  exactly  the  same  ether,  with  just  the  same 
peculiar  properties,  was  required  for  electricity  as  for  light. 
The  idea  of  some  such  medium  is  a  very  old  one  in  scientific 
speculation,  but  it  was  not  until  about  seventy  years  ago 
that  the  great  electrical  researches  of  Faraday  placed  it 
as  a  leading  article  of  faith  in  the  creed  of  the  scientist. 
About  thirty  years  later  came  the  epoch-making  work  of 
Clerk  Maxwell.  He  was  deeply  imbued  with  Faraday 's 


232 


LIGHT 


ideas,  but  had  the  great  advantage  of  being  a  skilled 
mathematician  as  well  as  a  physicist.  He  set  himself  the 
problem  of  considering  minutely  the  manner  in  which  a 
disturbance  would  be  propagated  in  the  ether.  Waves 
would  be  set  up  and  would  travel  with  a  certain  velocity, 
carrying  certain  electromagnetic  effects  along  with  them. 
In  free  space,  where  there  is  no  matter  and  nothing  but  ether, 
this  velocity  would  be  independent  of  the  frequency,  and 
Maxwell  showed  that,  if  his  theory  were  correct,  the  velocity 
could  be  expressed  in  terms  of  certain  quantities  that  could 
be  determined  by  electromagnetic  measurements.  This  ve- 
locity (v)  is  the  ratio  of  the  electromagnetic  to  the  electro- 
static unit  charge  of  electricity.  Maxwell's  electromagnetic 
theory  of  light  consists  in  the  statement  that  light-waves 
are  merely  electromagnetic  waves  that  have  a  frequency 
lying  within  certain  limits  determined  by  the  structure  of 
the  eye.  If  this  be  true,  the  velocity  of  light  (V)  in  free 
space  should  be  equal  to  the  quantity  that  we  have  de- 
noted by  v.  V  and  v  can  be  measured  by  direct  experi- 
ment. Here  are  some  of  the  results  expressed  in  millions 
of  centimeters  per  second,  with  the  names  of  the  experi- 
menters responsible  for  them.  The  variations  in  the  table 


F  (OPTICAL) 

v  (ELECTRICAL) 

Foucault    

.  29,836 

Ayrton  and  Perry    . 

29  600 

Cornu    

.  29,985 

Klemencic  •               .     . 

30  150 

Michelson  .         ... 

.  29  976 

Rosa  .         •         .     . 

29  993 

Newcoml)   .          .     .     . 

.  29  962 

Thomson  and.  Searls 

29  955 

show  that  it  is  difficult  to  measure  these  quantities  with 
very  great  precision,  but  there  is  no  evidence  that  shows 


LIGHT  AND  ELECTRICITY  233 

that  one  is  bigger  than  the  other.  The  presumption  is, 
therefore,  that  they  are  equal,  and  this  is  the  corner- 
stone on  which  the  electromagnetic  theory  of  light  is 
based. 

After  Maxwell,  the  next  great  step  was  made  by  Hertz 
about  twenty  years  ago.  He  succeeded  in  setting  up 
electric  waves  (some  of  them  about  a  foot  in  length, 
others  a  yard  or  more),  and  investigated  their  properties. 
His  famous  experiments  furnish,  perhaps,  the  most  strik- 
ing evidence  that  can  be  adduced  in  support  of  Maxwell's 
theory,  as  he  showed  that  these  electric  waves  obeyed 
exactly  the  laws  of  light,  as  Maxwell  had  predicted  they 
should.  He  found  that  they  were  reflected  so  that  the 
angle  of  reflection  was  equal  to  that  of  incidence.  He 
passed  them  through  a  large  prism  of  pitch  about  a  yard 
and  a  half  high,  and  showed  that  they  were  refracted  ac- 
cording to  SnelFs  law.  He  found,  too,  that,  just  as  with 
light- waves,  he  could  get  polarization  and  also  diffraction. 
The  determination  of  the  speed  with  which  the  waves 
were  propagated  was  a  matter  of  some  difficulty,  and  at 
first  it  appeared  that  they  did  not  travel  with  the  same 
velocity  as  does  light,  but  later  researches  have  shown 
conclusively  that  they  do.  Much  has  been  done  since 
Hertz's  first  experiments  to  clear  away  doubts  and  diffi- 
culties, and  now  an  almost  complete  analogy  between 
electrical  and  optical  phenomena  has  been  proved  by  ex- 
periment. Perhaps  I  should  say  in  passing  that  these 
electric  waves  that  Maxwell  saw  with  his  powerful  mind, 
and  whose  properties  he  predicted,  and  that  Hertz  made  a 
commonplace  in  every  physical  laboratory,  are  the  same 
waves  that  we  have  all  heard  so  much  about  in  more 
recent  times  as  employed  in  wireless  telegraphy.  They  are 


234  LIGHT 

popularly  associated  with  the  name  of  Marconi,  whose 
important  discovery  of  the  influence  of  a  "  grounded 
wire/'  immensely  extended  the  range  of  their  effective- 
ness. 

Let  us  turn  now  to  other  evidences  of  a  relation  between 
light  and  electricity.  It  has  been  stated  more  than  once 
that  in  free  ether;  where  there  is  no  matter,  the  velocity  of 
all  waves  must  be  the  same,  whatever  be  their  frequency, 
and  we  have  already  seen  that  there  is  a  good  agreement 
between  theory  and  observation  as  to  the  magnitude  of 
this  velocity.  When,  however,  matter  is  present,  the  speed 
of  the  wave  varies  with  the  frequency,  as  was  pointed  out 
at  some  length  in  the  lecture  on  dispersion.  In  that  lec- 
ture a  formula  was  given  connecting  the  refractive  index 
(ri),  which  determines  the  speed,  and  the  frequency  (/), 
and  if  we  refer  to  that  formula  (p.  66),  we  see  that  if  /  is 
zero,  so  that  there  are  no  vibrations  at  all,  and  everything 
is  steady,  we  then  have  n2=JL  Now  the  electromagnetic 
theory  indicates  that,  under  these  circumstances,  K  should 
be  what  is  known  as  the  specific  inductive  capacity  of  the 
substance  that  is  dealt  with.  This  can  be  determined 
from  purely  electrical  measurements,  and  it  is  important  to 
see  how  this  determination  agrees  with  its  value  obtained, 
in  accordance  with  our  theory,  from  optical  observations. 
The  two  substances  that  have  been  most  carefully  ex- 
amined from  this  point  of  view  are  Rock-salt  and  Fluorite. 
The  values  of  K  obtained  by  different  observers  from 
electrical  experiments  on  Rock-salt  were  as  follows  (the 
name  being  that  of  the  experimenter  quoted) :  Curie,  5.85; 
Thwing,  5.81;  Starke,  6.29;  the  mean  being  5.98.  The 
corresponding  numbers  for  Fluorite  are :  Curie,  6.8 ;  Romich, 
6.7;  Starke,  6.9;  of  which  the  mean  is  6.8.  The  values  of 


LIGHT  AND  ELECTRICITY 


235 


K,  calculated  from  optical  experiments  in  the  two  cases,  are 
5.9  and  6.8,  so  that  we  have  the  following  comparison :  — 


SUBSTANCE 

K  (OPTICAL) 

JT  (ELECTRICAL) 

Rock-salt            

5.9 

5.98 

Fluorite     

6.8 

6.8 

Theory  also  indicates  that  there  is  a  relation  between 
the  reflecting  power  of  a  metal  and  its  electrical  conduc- 
tivity, and  shows  that  the  reflecting  power  must  depend 
on  the  frequency.  By  observing  the  electrical  conduc- 
tivities of  different  metals,  we  are  able  to  predict  what 
their  reflecting  powers  should  be  for  a  given  frequency, 
and  to  test  the  theory  by  actual  measurements  of  these 
reflecting  powers.  The  following  table  sets  forth  some  of 
the  results,  the  numbers  expressing  the  percentage  of  the 
incident  light  that  is  reflected.  The  word  " light"  is  used 
in  rather  a  wide  sense,  for  the  frequencies  fi  and  /2  that  are 
dealt  with  are  so  low  that  the  waves  are  far  outside  the 
range  of  the  visible  portion  of  the  spectrum.  The  fre- 
quencies are  expressed  in  million  millions  per  second.  It 


METAL 

/i- 

35 

/•- 

i» 

OPTICAL 

ELECTRICAL 

OPTICAL 

ELECTRICAL 

Silver    

98.85 

98.7 

98  87 

98.85 

98.4 

98  6 

98  83 

98  73 

Zinc  *    . 

97  73 

97.73 

97  45 

97.47 

96.5 

96  5 

97  18 

97  04 

Nickel  

95.9 

96  4 

96  80 

96.84 

236  LIGHT 

will  be  observed  that  the  agreement  between  the  optical 
and  electrical  estimates  of  the  reflecting  power  is  better 
for  /2  than  for  /x.  The  explanation  of  this  is  that  the 
theoretical  formula  employed  in  the  computation  is  only 
approximately  true,  the  approximation  being  closer  for 
small  frequencies  than  for  large  ones. 

The  various  types  of  evidence  for  an  intimate  relation 
between  light  and  electricity  that  have  so  far  been  referred 
to  are  all  of  a  somewhat  indirect  character,  and  it  would 
seem  reasonable  to  suppose  that  there  should  be  some 
phenomena  that  would  prove  more  directly  that  light  and 
electricity  have  something  in  common.  I  have  now  to 
direct  your  attention  to  evidence  of  this  class.  The  most 
elementary  knowledge  of  the  science  of  electricity  will 
make  it  clear  that  there  is  a  very  close  relation  between 
electricity  and  magnetism.  It  shows,  for  example,  that 
an  electric  current  gives  rise  to  a  magnetic  field,  and  that 
a  piece  of  iron  can  be  magnetized  by  passing  an  electric 
current  round  it.  If,  then,  light  and  electricity  are  in  any 
sense  one,  we  should  expect  a  magnetic  field  to  have  some 
influence  on  light,  and  one  of  Faraday's  epoch-making 
discoveries  proved  that  this  is  the  case.  Faraday  found 
that  when  such  a  uniform  transparent  substance  as  glass 
or  carbon  bisulphide  is  placed  in  a  powerful  magnetic  field, 
and  a  beam  of  plane  polarized  light  is  made  to  traverse 
the  field  in  the  direction  of  the  lines  of  magnetic  force, 
the  plane  of  polarization  is  rotated.  When  we  dealt  in  an 
earlier  lecture  with  a  kindred  phenomenon  exhibited  by 
quartz,  solutions  of  sugar,  and  other  optically  active  media, 
we  saw  that  the  rotation  could  be  explained  once  we  un- 
derstood why  a  wave  circularly  polarized  in  the  clockwise 
sense  should  move  through  the  medium  with  a  different 


LIGHT  AND  ELECTRICITY  237 

speed  than  one  polarized  counter-clockwise.  The  same 
problem  presents  itself  in  the  explanation  of  the  Faraday 
effect;  but  the  solution  must  be  quite  different,  for  here 
we  have  no  peculiarities  of  structure  to  deal  with  that  can 
distinguish  the  right  hand  from  the  left  when  rotations 
are  concerned.  In  this  case  the  explanation  is  afforded 
by  the  application  of  certain  well-known  laws  of  electro- 
magnetism  which  deal  with  the  mutual  influence  of  a  cur- 
rent and  a  magnetic  field,  and  show  that  different  effects 
are  produced  by  currents  flowing  in  opposite  senses,  clockwise 
and  counter-clockwise.  A  precise  form  is  given  to  the 
investigation  by  the  adoption  of  the  electron  theory, 
which  has  already  been  referred  to.  According  to  this 
the  atoms  of  a  substance  are  made  up  of  groups  of 
electrons,  which  constitute  small  charges  of  electricity, 
and,  when  moving  round  an  orbit,  have  some  of  the 
characteristics  of  an  electric  current.  A  careful  analysis 
shows  that  a  right-handed  circularly  polarized  beam 
should  cross  the  magnetic  field  at  a  different  rate  than 
a  left-handed  one,  so  that  a  rotation  of  the  plane  of 
polarization  is  to  be  expected.  It  also  appears  that  the 
amount  of  the  rotation  is  directly  proportional  to  the 
length  of  the  field  traversed,  a  law  that  is  similar  to  that 
which  governs  the  behavior  of  optically  active  media,  and 
one  that,  like  it,  has  been  amply  verified  by  experiment. 
The  theory  also  indicates  that  the  amount  of  the  rotation 
depends  upon  the  frequency,  so  that  we  have  rotatory 
dispersion,  as  in  the  case  of  active  media.  The  following 
table  records  the  rotations  produced  by  creosote  and  car- 
bon bisulphide  for  different  lines  in  the  spectrum,  and 
compares  the  observed  values  with  the  predictions  of 
theory :  — 


238 


LIGHT 


CREOSOTE 

CAKIJON  BISULPHIDE 

T 

SPECTRUM 

ROTATION 

ROTATION 

ROTATION 

ROTATION 

(theory) 

(observation) 

(theory) 

(observation) 

c 

0.573 

0.573 

0.592 

0.592 

D 

0.744 

0.758 

0.760 

0.760 

E 

0.987 

1.000 

0.996 

1.000 

F 

1.222 

1.241 

1.225 

1.234 

G 

1.723 

1.723 

1.704 

1.704 

Wood  gives  the  following  results  for  the  rotations  pro- 
duced by  sodium  vapor  for  different  frequencies  in  the 
neighborhood  of  the  natural  frequencies  of  sodium.  The 
frequencies  (/)  are  given  in  million  millions  per  second,  and 
the  rotations  (R)  are  those  observed,  or  calculated,  to  the 
nearest  degree :  — 


/ 

R  (THEORY) 

R  (OBSERVATION) 

/ 

R  (THEORY) 

R  (OBSERVATION) 

501 

5 

5 

510 

93 

90 

504 

10 

10 

511 

43 

43 

505 

23 

20 

512 

41 

40 

506 

38 

40 

513 

20 

20 

507 

59 

66 

514 

9 

10 

508 

89 

90 

516 

5 

5 

Theory  also  indicates,  and  experiment  verifies,  that 
rotation  is  in  the  same  absolute  direction  when  the  light 
is  travelling  from  A  to  B  as  from  B  to  A.  Thus  if,  to  a 
person  at  A  looking  towards  B,  the  rotation  appears  to  be 
clockwise  when  the  light  goes  from  A  to  #,  then  if  the 
light  be  reflected  from  B  so  as  to  return  to  A}  the  rotation 


LIGHT  AND  ELECTRICITY 


239 


will  still  appear  to  A  to  be  clockwise.  This  leads  to  a 
somewhat  curious  result.  The  path  of  a  ray  of  light,  no 
matter  how  crooked  it  may  be,  is  usually  reversible.  If 
A  can  see  B,  then  B  can  see  A,  and  this  is  true  whether 
they  look  at  one  another  directly,  or  whether  the  light  be 
reflected  and  refracted  at  various  points  in  the  passage 

from  one  to  another.    You 

& 
may  not  be  able  to  see  a  per-     { 

son  directly,  and  yet  you 
may  have  a  clear  view  of  him 
by  reflection  in  a  mirror ;  but 
if  this  be  so,  you  know  that 
he  also  can  see  you  in  the 
mirror.  Thus,  by  no  ordi- 
nary optical  device  can  A  see 
B  without  B  being  able  also 
to  see  A.  However,  by  util- 
izing this  power  of  rotating 
the  plane  of  polarization  possessed  by  a  magnetic  field,  it  is 
possible  to  think  of  an  arrangement  by  means  of  which  B 
could  see  A,  while  A  could  not  see  B.  Take  two  Nicol 
prisms  and  set  them  with  their  principal  planes  ON1  and 
ON2  (Fig.  69)  inclined  at  an  angle  of  45°.  Place  them  in 
a  medium  in  a  magnetic  field  that  has  just  the  necessary 
strength  to  turn  the  plane  of  polarization  counter-clockwise, 
say,  through  an  angle  of  45°.  The  light  that  goes  from  A 
passes  through  the  first  Nicol  and  then  is  plane  polarized, 
the  plane  of  its  polarization  being  parallel  to  ON^  After 
passing  across  the  magnetic  field,  this  plane  is  rotated 
through  45°,  and  so  is  parallel  to  ON%.  The  light  is  thus 
polarized  just  in  the  right  plane  to  pass  freely  through 
the  second  Nicol,  so  that  it  reaches  B,  who  will  therefore 


FIG.  69 


240  LIGHT 

have  no  difficulty  in  seeing  A.  Now  think  of  the  light 
that  sets  out  from  B  towards  A.  On  passing  through  the 
first  Nicol  that  it  reaches,  it  will  be  plane  polarized,  with 
the  plane  of  its  polarization  parallel  to  ON2.  It  then 
enters  the  magnetic  field  and,  in  crossing  it,  has  the  plane 
of  its  polarization  rotated  45°  in  the  direction  indicated  in 
the  figure.  Thus  the  light  is  polarized  in  the  direction  Oa, 
which  is  at  right  angles  to  ONV  so  that  the  light  cannot 
get  through  the  Nicol  to  reach  A.  Hence  B  sees  A  with- 
out A  seeing  B. 

The  Faraday  effect  with  which  we  have  been  dealing 
was  the  first  thing  of  the  kind  discovered  that  exhibited 
a  direct  action  of  magnetism  on  light,  but  there  have 
been  several  similar  discoveries  since.  Thus,  about  thirty 
years  ago,  Kerr  found  that  plane  polarized  light  is  con- 
verted into  elliptically  polarized  light  when  it  is  reflected 
from  the  polished  pole  of  an  electromagnet,  under  circum- 
stances in  which  this  change  could  not  occur  if  the  field 
were  not  magnetic.  A  few  years  earlier  the  same  experi- 
menter had  discovered  another  interesting  relation  between 
optical  and  electrical  phenomena.  He  found  that  a  dielec- 
tric, like  glass,  or  even  a  liquid,  such  as  carbon  bisulphide, 
behaves  quite  differently  when  in  a  powerful  electric  field 
than  when  it  is  not  so  placed.  It  acquires  the  doubly 
refracting  properties  of  a  crystal.  This  seems  to  indicate 
that  the  electric  field  has  the  effect  of  arranging  the  elec- 
trons in  order,  and  so  of  producing  something  like  the 
definite  structure  that  gives  a  crystal  different  optical 
qualities  in  different  directions,  and  accounts  for  its  doubly 
refracting  power. 

Even  more  interesting  than  the  Kerr  effect  is  that  of 
Zeeman,  discovered  in  1896.  He  found  that  a  magnetic 


LIGHT  AND  ELECTRICITY  241 

field  could  alter  the  positions  and  the  character  of  certain 
lines  in  the  spectrum.  This  is  a  very  significant  fact,  if 
you  bear  in  mind  what  has  been  said  as  to  the  position  of 
a  line  in  the  spectrum  and  its  relation  to  the  frequency  of 
the  vibrations  going  on  within  the  atom.  To  alter  the 
frequency,  you  must  interfere  with  the  mechanism  of  an 
atom,  and  Zeeman's  discovery  proves  that  you  can  do 
this  merely  by  placing  the  atom  in  a  strong  magnetic 
field.  In  view  of  the  well-known  influence  of  magnetic 
forces  on  electric  currents,  we  may  find  in  the  Zeeman 
effect  a  powerful  support  for  the  electric  theory  of  matter 
that  is  a  leading  feature  of  recent  speculation,  and  it  is 
mainly  because  of  this  that  the  phenomenon  has  received 
so  much  attention  from  the  world  of  physical  science. 
Let  us  see,  somewhat  more  clearly,  what  the  Zeeman 
effect  is  (at  least  in  its  simplest  aspect),  and  then  consider 
the  general  outlines  of  the  explanation  that  has  been  sug- 
gested. We  have  been  reminded  that  when  light  from  a 
luminous  body  in  the  form  of  vapor  is  viewed  through  a 
spectroscope,  the  spectrum  is  crossed  by  certain  bright 
lines  which  have  definite  and  fixed  positions  for  any  given 
substance  in  a  given  condition.  So  well  fixed  and  well 
known  are  these  lines  that,  as  has  been  seen,  we  may 
readily  determine  the  nature  of  a  substance  by  noting 
carefully  the  positions  of  these  lines.  Zeeman's  striking 
discovery  was  that,  when  the  luminous  body  was  placed 
in  a  strong  magnetic  field,  a  single  line  was  replaced  in 
some  cases  by  two  lines,  one  on  each  side  of  the  position 
of  the  original  line ;  in  other  cases  by  three  lines,  one  in 
the  position  of  the  original,  and  one  on  each  side  thereof. 
Later  researches  have  revealed  more  complicated  cases, 
but  we  shall  confine  our  attention  to  those  that  are  simplest. 


242 


LIGHT 


Without  entering  too  much  into  technicalities,  let  me 
indicate  the  explanation  afforded  by  Lorenz  of  the  simplest 
case  of  the  Zeeman  effect.  The  fundamental  idea  is  that 
which  lies  at  the  root  of  the  electric  theory  of  matter.  It 
supposes  that,  in  its  last  analysis,  an  atom  of  matter 
would  be  found  to  consist  of  a  number  of  moving  charges 
of  electricity,  which  now  usually  go  by  the  name  of  elec- 
trons. Theory  indicates  and  experience  proves  that  a 


FIG.  70 

charge  of  electricity  moving  rapidly  round  a  closed  orbit 
has  an  effect  similar  to  that  of  an  electric  current  flowing 
in  the  same  circuit.  Now  it  is  one  of  the  most  widely 
known  and  most  firmly  established  laws  of  electromag- 
netism  that  a  current  is  affected  by  the  presence  of  a  mag- 
netic field,  so  that  we  have  good  reason  to  suppose  that 
an  electron  moving  in  an  orbit  would  be  affected  by  such 
a  field.  Moreover,  certain  laws  of  electromagnetism  that 
are  well  grounded  in  experience  enable  us  to  predict  how 
the  electron  would  be  affected  in  any  given  circumstances. 
Consider  the  simple  case  of  an  electron  moving  steadily  in 
a  circle,  say  in  the  plane  of  this  paper  round  0  as  a  center. 
(Fig.  70.)  As  the  electron  might  move  round  in  two 
senses,  clockwise  or  counter-clockwise,  there  will  be  two 
cases  to  deal  with,  and  we  may  distinguish  these  electrons 
by  the  letters  E1  and  Ez.  If  the  magnetic  force  is  at  right 


LIGHT  AND  ELECTRICITY  243 

angles  to  the  plane  of  the  paper,  it  follows  from  the  laws 
of  electromagnetism  that  E1  will  be  driven  along  OElt 
away  from  the  center,  while  E2  will  be  pulled  along  E%0 
towards  the  center.  It  is  a  simple  deduction  from  this  that 
the  frequency  of  the  vibrations  of  E2  will  be  increased, 
while  that  of  El  will  be  diminished.  You  know,  doubt- 
less, that  if  you  make  a  stone  describe  a  circle  by  whirling 
it  round  at  the  end  of  a  string,  the  force  with  which  you 
have  to  pull  the  string  is  greater,  the  greater  the  number 
of  revolutions  per  minute,  i.e.  the  greater  the  frequency. 
Thus  an  increased  force  towards  the  center  means  a  greater 
frequency  and  a  diminished  force  towards  the  center  means 
a  smaller  frequency.  Now  when  there  are  no  external 
magnetic  forces  present  the  electrons  E1  and  E%  are  drawn 
towards  0  with  a  certain  force  that  depends  on  the  distri- 
bution of  the  electrons  in  that  neighborhood.  The  pres- 
ence of  a  magnetic  field  adds  a  new  force  away  from  0  in 
the  case  of  E1}  and  towards  0  in  the  case  of  Ez,  so  that 
the  total  force  towards  0  is  diminished  for  E1  and  in- 
creased for  $2,  and  thus  the  frequency  is  diminished 
for  E1  and  increased  for  E2.  It  thus  appears  that  the 
effect  of  placing  a  number  of  rotating  electrons  in  a  mag- 
netic field  would  be  that  those  electrons  whose  planes  of 
motion  were  at  right  angles  to  the  lines  of  magnetic  force 
would  have  their  frequencies  increased  or  diminished 
according  to  the  sense  (clockwise  or  counter-clockwise)  in 
which  their  orbits  were  described.  Thus  the  original  single 
line  in  the  spectrum  would  be  replaced  by  a  doublet,  the 
members  of  which  would  be  on  opposite  sides  of  the  original 
line.  At  the  same  time  those  electrons  that  were  mov- 
ing in  the  same  plane  as  the  lines  of  magnetic  force  would 
not  be  affected,  so  that  their  frequency  would  be  un- 


244  LIGHT 

changed.  Not  only  does  Lorenz's  explanation  account  for 
the  main  feature  of  the  phenomenon,  that  is,  for  the  pro- 
duction of  two  or  of  three  lines  from  a  single  line,  accord- 
ing to  the  direction  of  the  lines  of  magnetic  force,  but  it 
also  indicates  the  state  of  polarization  of  the  different  lines. 
It  shows  that  the  two  lines  of  a  doublet  should  be  circu- 
larly polarized,  one  being  right-handed  and  the  other  left- 
handed.  It  shows  also  that  with  a  triplet  the  middle  line 
should  be  polarized  in  a  plane  perpendicular  to  the  direc- 
tion of  the  magnetic  force,  and  the  two  outer  lines  polar- 
ized in  a  plane  parallel  to  that  direction.  All  these  de- 
tails with  reference  to  the  nature  of  the  polarization  of  the 
different  lines  were  first  predicted  by  Lorenz's  theory,  and 
later  observation  proved  them  to  be  correct. 

It  should  perhaps  be  stated  that  later  researches  have 
proved  that  in  many  instances  the  influence  of  a  magnetic 
field  on  the  character  of  the  spectral  lines  is  much  more 
complex  than  what  was  first  observed  by  Zeeman.  There 
are  many  indications  that  if  an  atom  be  rightly  regarded 
as  a  group  of  electrons,  the  distribution  and  motion  of 
these  must  constitute  a  mechanism  that  is  far  from  simple, 
and  the  complexity  of  certain  aspects  of  the  Zeeman  effect 
is  what  might  well  be  expected.  It  would  be  out  of  place 
to  enter  into  such  questions  here,  but  before  taking  leave 
of  the  Zeeman  effect  I  should  like  to  call  your  attention 
to  a  very  interesting  application  of  the  theory  that  has 
been  made  quite  recently  by  Hale.  It  has  long  been 
known  that  there  is  an  intimate  relation  between  electricity 
and  magnetism.  You  have  been  reminded  within  the  last 
few  minutes  of  the  influence  on  a  current  of  a  magnetic 
field,  and  you  know  probably  that  a  current  by  itself  sets 
up  a  magnetic  field,  that  is,  that  there  are  certain  mag- 


LIGHT  AND  ELECTRICITY  245 

netic  effects  due  merely  to  the  presence  of  an  electric 
current.  If,  then,  a  moving  charge  of  electricity  is,  under 
any  circumstances,  equivalent  to  a  current,  it  should  also 
give  rise  to  a  magnetic  field,  as  Maxwell  anticipated  and 
as,  in  fact,  Rowland  proved  by  experiment  as  long  ago 
as  1876.  Now  the  ingenious  device  of  Hale  referred  to  on 
p.  88  of  the  lecture  on  Spectroscopy,  by  means  of  which 
he  takes  photographs  of  the  Sun  with  light  from  a  single 
line  in  the  spectrum,  e.g.  one  of  the  lines  of  hydrogen, 
quickly  led  in  his  hands  to  many  interesting  discoveries. 
It  made  it  clear,  amongst  other  things,  that  there  are 
numerous  vortices  or  whirlwinds  in  the  solar  atmosphere, 
and  such  is  the  detail  in  some  of  the  photographs  that  it 
seems  possible  to  determine,  from  the  form  of  the  streamers 
round  the  whirlwind,  in  what  sense  (clockwise  or  counter- 
clockwise) the  vortex  is  rotating.  These  whirlwinds  are 
characteristic  of  Sun-spots,  and  it  seems  probable  that  all 
such  spots  are  vortices  spinning  in  the  solar  atmosphere. 

We  know  from  numerous  terrestrial  experiments  that  at 
high  temperatures  carbon  and  many  other  elements  that 
occur  in  the  Sun  send  out  large  numbers  of  corpuscles 
charged  with  electricity.  It  is  natural  to  suppose  that  the 
same  thing  will  happen  under  similar  circumstances  in  the 
Sun.  Let  us  suppose,  further,  that  in  any  region  near  a 
Sun-spot  a  preponderance,  say,  of  negative  charges  exists. 
These  will  be  whirled  round  in  the  vortex,  and  as  they 
move  round  will  constitute  effectively  an  electric  current, 
and  so  give  rise  to  a  magnetic  field.  We  should  expect, 
then,  that  if  our  hypotheses  be  justifiable,  a  Sun-spot 
should  be  characterized  by  the  presence  of  a  magnetic 
field.  One  way  of  detecting  this  presence  is  to  make  care- 
ful observations  of  the  features  of  the  lines  of  the  spectrum 


246  LIGHT 

in  this  region,  and  see  if  we  can  find  evidence  of  the  Zee- 
man  effect.  It  had  been  known  for  some  time  that  the 
spectrum  of  a  Sun-spot  differs  in  several  respects  from  the 
ordinary  solar  spectrum.  Amongst  the  peculiarities  of  a 
Sun-spot  spectrum  are  two  that  are  specially  significant  in 
view  of  the  Zeeman  effect :  in  the  first  place,  a  large  num- 
ber of  doublets,  or  double  lines,  exist ;  and  secondly,  many 
of  the  lines  are  unusually  broad.  These  are  just  the 
features  that  we  should  expect,  from  our  knowledge  of  the 
Zeeman  effect,  provided  we  see  the  force  of  the  reasons 
that  have  been  adduced,  or  of  any  other  reasons,  for  ex- 
pecting a  strong  magnetic  field  near  a  Sun-spot  rather 
than  in  other  regions  of  the  Solar  atmosphere. 

Prompted  by  some  such  reasons  as  these,  Hale  recently 
devoted  the  resources  of  the  Mt.  Wilson  Observatory  to 
the  problem  of  examining  the  spectral  lines  in  Sun-spots, 
keeping  an  especially  sharp  lookout  for  evidences  of  the 
Zeeman  effect.  He  found  that  the  light  from  the  two  edges 
of  certain  lines  was  circularly  polarized  in  opposite  direc- 
tions. He  found  that  right-  and  left-handed  polarizations 
were  interchanged  in  passing  from  a  vortex  spinning  clock- 
wise to  one  spinning  in  the  opposite  sense.  He  found  also 
that  the  displacements  of  the  widened  lines  had  just  the 
same  features  as  those  detected  by  Zeeman.  With  the 
caution  of  a  man  of  science  he  concluded  that  the  existence 
of  a  magnetic  field  in  Sun-spots  was  "probable."  By  ex- 
perimenting in  his  laboratory  on  the  strength  of  field 
necessary  to  produce  a  shift  of  the  spectral  lines  of  the 
same  amount  as  those  observed  in  the  Sun-spots,  he  was 
enabled  to  form  some  estimate  of  the  strength  of  the 
magnetic  field  in  these  spots. 

Here,  then,  we  have  a  striking  example  of  the  breaking 


LIGHT  AND  ELECTRICITY  247 

down  of  barriers  that  earlier  thinkers  have  set  up  be- 
tween different  fields  of  knowledge.  Astronomy,  chemis- 
try, electricity,  magnetism,  and  light  have  each  had  fences 
raised  around  them.  In  these  researches  of  Hale's  yoiT 
have  observations  that  seem  to  deal  only  with  light,  obser- 
vations, namely,  of  the  varying  intensity  of  the  light  in 
different  places.  Some  portions  of  the  field  of  view  are 
very  bright,  others  seem  relatively  dark,  and  present  the 
appearance  of  dark  lines  of  different  widths  in  different 
positions.  From  these  you  are  enabled  to  determine  cer- 
tain facts  of  astronomy,  to  learn  something  definite  as  to 
the  physical  condition  of  the  Sun.  You  also  learn  some- 
thing of  chemistry,  for  you  can  tell,  with  practical  certainty, 
that  you  are  looking  at  iron,  or  chromium,  or  manganese, 
or  vanadium.  Electricity,  too,  is  brought  before  your 
view,  for  you  are  forced  to  consider  the  effect  of  electric 
charges  caught  up  in  the  whirl  of  the  great  solar  vortices. 
Finally,  these  observations  on  light  lead  you  inevitably 
into  the  field  of  magnetism,  and  even  enable  you  to  esti- 
mate the  strength  of  the  magnetic  forces  that  play  about 
the  surface  of  the  Sun,  although  they  are  nearly  a  hundred 
million  miles  away. 

Thus  science  is,  after  all,  a  unity,  and  in  this  key  I 
may  appropriately  bring  this  course  of  lectures  to  a  close. 
Science  strives  to  bring  all  things,  with  whatever  names 
they  may  have  been  labelled  in  the  past,  into  harmony 
with  some  all-pervading  principle  or  law.  "Give  me 
extension  and  motion/'  exclaimed  Descartes,  "and  I  will 
construct  the  world !"  "Give  me  ether  and  electrons  and 
the  fundamental  laws  of  mechanics,"  says  the  modern 
physicist,  "and  I  will  give  you  a  picture  of  the  world  that 
is  beautiful  in  its  simplicity  and  in  its  faithfulness.  I  will 


248  LIGHT 

not,  however,  pretend  to  explain  the  world,  and  I  will 
leave  questions  of  reality  and  of  purpose  for  others 
to  dispute  over."  Perhaps  it  should  be  remarked  that 
this  method  of  the  modern  man  of  science  differs  essen- 
tially from  what  is  sometimes  called  the  metaphysical 
method.  I  have  no  intention  of  saying  anything  against 
metaphysics.  It  would  be  an  impertinence  to  do  so,  and 
I  am  ready  to  admit  that  the  remarks  of  scientists  about 
metaphysicians  are  often  quite  as  valueless  as  those  of 
metaphysicians  about  science.  All  that  need  be  said  is 
that  physicists  do  not  even  attempt  to  evolve  the  laws 
that  govern  the  world  from  their  own  consciousness. 
Their  knowledge  is  strictly  empirical,  their  hypotheses  and 
"laws"  are  valued  only  so  far  as  they  harmonize  experi- 
ences and  fit  the  facts  together.  Everywhere  these  laws 
must  be  put  to  this  test,  and  if  they  fail  to  satisfy  it,  they 
must  be  ruthlessly  abandoned.  My  aim  throughout  has 
been  to  show  you  how  well  the  modern  theory  of  light 
serves  its  purpose  and  actually  fits  the  facts,  and  I  hope 
that  I  have  succeeded  in  giving  you  some  conception  of  its 
comprehensiveness  and  power,  even  if  I  have  not  revealed 
its  true  nature  as  a  noble  work  of  art. 


INDEX 


Aberration,  spherical,  148. 

Absorption,  48-58;  of  energy,  53; 
in  lenses,  150;  dark  lines  due  to, 
80 ;  spectra,  81 ;  Hartley  on,  83. 

Abstractions,  123-125. 

Amplitude,  defined,  26,  122 ;  and  in- 
tensity, 127. 

Arago,  99. 

Aristotle,  9. 

Art  and  Science,  1,  4-6,  45,  46,  248. 

Atom,  nature  of,  53;  vibrations 
within,  55,  79;  arrangement  in 
space,  83,  110-113. 

Autochrome  plate,  42. 

Balmer,  56. 
Biot,  109. 

Brewster,  law  as  to  polarizing  angle, 
129 ;  objection  to  wave  theory,  207. 
Bunsen,  spectrum  analysis,  77. 

Cauchy,  on  dispersion,  62-65. 

Chromatic  effects  in  telescopes,  148, 
151. 

Color,  relation  to  frequency,  26 ;  equa- 
tion, 27 ;  primary,  27 ;  vision,  28- 
32 ;  photography,  33-46,  170-174. 

Conical  refraction,  185. 

Critical  angle,  16,  120. 

Crookes,  spectrum  analysis,  177. 

Crystal,  index  surface  in,  179;  opti- 
cal properties  of,  175—201 ;  optic 
axis  of,  178;  ordinary  and  ex- 
traordinary rays  in,  180;  positive 
and  negative,  179;  rings  and 
crosses  with,  190-201 ;  rotatory 
power,  104 ;  structure  of,  104,  107. 

Dark  lines  in  spectrum,  due  to  ab- 
sorption, 54,  55. 

Darwin,  4,  93 ;  his  Origin  of  Species, 
91. 

Descartes,  247. 


Diffraction,  202-228 ;  dynamical 
theory  of,  209;  Fresnel  on,  212, 
213;  Lommel  on,  216-218;  grat- 
ings, 220. 

Dispersion,  meaning  of,  47;  theory 
of,  59-69;  anomalous,  69;  appli- 
cations of,  88. 

Doppler's  principle,  84-87. 

Double  refraction,  176. 

Doublets,  57. 

Elastic  solid  theory,  125. 
Electricity,  its  relation  to  light,  229- 

248. 

Electric  waves,  232. 
Electrons,  53,  242,  247. 
Energy,  53. 
Ether,  nature  of,  99,   100,   121,   124, 

125 ;  in  a  crystal,  175 ;  in  electrical 

science,  231. 
Evolution,  91-93. 
Extraordinary  ray,  180. 
Eye,  as  optical  instrument,  141. 
Eye-piece,  152. 

Faraday,  23;  electrical  researches, 
231 ;  effect  of  magnetism  on  light, 
236,  237. 

Fischer,  on  optical  activity,  114,  115. 

Fraunhofer,  80. 

Frequency,  defined,  26;  relation  to 
color,  26 ;  natural,  48-51 ;  forced, 
48—51 ;  of  vibrations  within  atoms, 
55 ;  relation  to  period  and  wave 
length,  155;  limits  of  eye's  sensi- 
tiveness, 70. 

Fresnel,  idea  of  ether,  99,  100;  on 
interference,  161,  162;  biprism, 
162;  on  diffraction,  212,  213. 

Geometrical  shadow,  205. 
Gernez,  on  optical  activity,  110. 
Greek  science,  7-9. 


249 


250 


INDEX 


Hale,  method  of  photographing  prom- 
inences and  flocculi,  88-91 ;  his 
spectroheliograph,  88;  his  investi- 
gations on  Sun-spots,  244-247. 

Hamilton,  on  conical  refraction, 
185. 

Hartley,  83. 

Helmholtz,  23;  on  color  vision,  28- 
31 ;  on  Young,  157. 

Hering,  on  color  vision,  28,  31. 

Herschel,  on  rotatory  power,  104. 

Hertz,  on  electric  waves,  233. 

Huggins,  on  nebulae,  76 ;  method  of 
viewing  solar  prominences,  87. 

Huyghens  principle,  208,  209. 

Index  surface,  179. 

Intensity  of  reflected  light,  127; 
ratio  of  intensities,  132 ;  influence 
of  layer  of  transition  on,  130,  131 ; 
from  metals,  136 ;  reflecting  power 
and  electrical  conductivity,  235. 

Interference,  Principle  of,  34,  154- 
174;  Young  on,  157-160;  Fresnel 
on,  161,  162;  Lloyd  on,  161;  color 
due  to,  163,  166-170;  stationary 
waves  produced  by,  172,  173;  ap- 
plication to  diffraction,  209;  to 
gratings,  222. 

Kayser  and  Runge,  56. 
Kerr  effect,  240. 
Kirchhoff,  80,  81. 

Least  action,  140. 

Le  Bel,  112. 

Lippman,    color    photography,    34, 

170-174. 

Lommel  on  diffraction,  216-218. 
Lorenz,  on  Zeeman  effect,  242-244. 
Lumiere,  color  photography,  42-44. 

Magnetism  and  light,  Faraday  effect, 
236-239;  Kerr  effect,  240;  Zee- 
man effect,  240-246. 

Marconi  electric  waves,  234. 

Maxwell,  23;  theory  of  color  vision, 
28;  color  photography,  34;  on 
Saturn's  rings,  87;  electromagnetic 
theory  of  light,  231,  232 ;  on  mag- 
netic effects  of  a  moving  electric 
charge,  245. 


Method  of  science,  10,  13,  14,  206, 
207,  247. 

Michelson,  spectroscope,  75;  visi- 
bility curves,  78,  79 ;  wave-lengths 
as  standards,  226. 

Morse,  58. 

Nebula,  nature  of,  76. 

Newton,  on  color,  9;  greatness  of, 
13,  21-23;  his  "Opticks,"  13,  20, 
166,  205 ;  his  method,  13,  14 ;  his 
experiments,  14-21 ;  on  soap- 
bubbles,  164;  his  rings,  166-169; 
on  diffraction,  205,  206;  on 
shadows,  205,  206;  objection  to 
wave  theory,  205. 

Nicol's  prism,  explanation  of  its 
action,  177,  178;  used,  95,  99,  102, 
103,  116,  177,  191. 

Objective,  149,  152. 

Optical  activity,  104-117;  Biot,  109; 

Gernez,  110;  Pasteur,  110;   Van't. 

Hoff  and   Le   Bel,    112;    Fischer, 

114,  115. 
Optic  axis,  178. 
Ordinary  ray,  180. 

Pasteur,  on  optical  rotation,  110. 

Period,  155. 

Phase,  meaning  of,  122;  difference 
of,  122;  for  reflection  from  trans- 
parent substances,  134 ;  for  total 
reflection,  134,  135;  for  reflection 
from  metals,  137;  influence  on 
interference,  156. 

Photography,  ordinary,  35-37 ;  color, 
33-46;  direct  methods,  33;  in- 
direct methods,  33;  Maxwell  on, 
34;  difficulties  of,  41;  Lippman's 
process,  170-174;  Lumiere 's 
process,  42-44;  defects  of,  44,  45; 
relation  to  art,  45,  46. 

Pickering,  57. 

Plato,  8. 

Polarization,  95-117;  different  kinds 
of,  97,  98;  mechanical  analogues, 
100,  101,  177 ;  effect  on  intensity  of 
reflection,  127 ;  plane  of,  in  crystals, 
188;  rotatory,  102-117,  236-239. 

Polarizing  angle,  129 ;  Brewster's  law, 
129 ;  quasi,  137 ;  in  crystals,  187. 


INDEX 


251 


Rays  in  crystals,  184. 

Reflection,  fact  of,  10,  11;  laws  of, 
10,  11,  118-153;  from  metals,  136; 
illustrating  principle  of  least  action, 
139,  140;  total,  10,  11,  120,  135. 

Refraction,  fact  of,  10,  11;  laws  of, 
9,  11,  118-153;  illustrating  princi- 
ple of  least  action,  139,  140; 
double,  176. 

Refractive  index,  meaning  of,  120 ; 
in  crystals,  179-182;  measured 
electrically,  234. 

Reversal,  81. 

Rings  and  crosses  formed  with 
crystals,  190-201. 

Rotatory  polarization,  structural, 
102,  103;  magnetic,  236-239. 

Rowland,  grating,  75;  map  of 
spectra,  80;  on  magnetic  effect  of 
moving  electric  charge,  245. 

Ruskin,  4-6. 

Saturn's  rings,  87. 

Science,  aim  of,  118,  121,  123,  186, 
248;  alleged  inhumanity,  3;  rela- 
tion to  art,  1,  4,  5,  6;  early,  7-12; 
language  of,  24 ;  divisions  of,  229  ; 
method  of,  10,  13,  14,  206,  207, 
247. 

Secondary  spectra,  151. 

Shadows,  geometrical,  205;  Newton 
on,  205,  206. 

Singular  points,  185. 

Snell,  9. 

Soap-bubbles,  164,  165. 

Solar  prominences,  85,  87. 

Solar  vortices,  245. 

Spectrograph,  76. 

Spectroheliograph,  88,  89. 

Spectroscope,  74,  75. 

Spectroscopy,  70-94. 


Spectrum,  15;  dark  lines  in,  54-57, 
80;  bright  lines  in,  71,  74;  con- 
tinuous, 72,  73,  76;  band,  57; 
produced  by  gratings,  227. 

Spherical  aberration,  148. 

Stellar  evolution,  91-93. 

Stokes,  23 ;  on  absorption  lines,  80 ; 
theory  of  diffraction,  209. 

Sun-spots,  85,  245,  246. 

Superposition,  principle  of,  155,  156. 

Telescope,  purpose  of,  142;  form, 
143;  material,  144;  size,  145; 
arrangement  of  parts,  147 ;  defects, 
148-150;  objectives,  149,  152; 
eye-piece,  152. 

Transition  from  one  medium  to  an- 
other, 126,  127,  129,  134. 

Turner,  5. 

Van't  Hoff,  112. 

Vibrations,  transverse,  TS,  99;  longi- 
tudinal, 98,  99 ;  confined  to  wave- 
front,  97,  99. 

Visibility  curves,  78,  79. 

Vision,  limits  of,  27,  30,  70;  theory 
of  color,  28-32. 

Watts,  Marshall,  58. 

Wave,    25;     length,    154,    220-228; 

front,  96;    theory,  121,  205,  207; 

surface,  182-185 ;  different  theories, 

123,  154 ;  stationary,  173 ;  electric, 

232-234. 
Wood,  238. 
Wordsworth,  21. 

Young,  on  color  vision,  28-31 ;  on 
interference,  157-161. 

Zeeman  effect,  240-246. 


THE  COLUMBIA  UNIVERSITY  PRESS 

Columbia  University  in  the  City  of  New  York 


The  Press  was  incorporated  June  8,  1893,  to  promote  the  pub- 
lication of  the  results  of  original  research.  It  is  a  private  corpora- 
tion, related  directly  to  Columbia  University  by  the  provisions  that 
its  Trustees  shall  be  officers  of  the  University  and  that  the  Presi- 
dent of  Columbia  University  shall  be  President  of  the  Press. 


The  publications  of  the  Columbia  University  Press  include  works 
on  Biography,  History,  Economics,  Education,  Philosophy,  Lin- 
guistics, and  Literature,  and  the  following  series : 

Columbia  University  Biological  Series. 

Columbia  University  Studies  in  Classical  Philology. 

Columbia  University  Studies  in  Comparative  Literature. 

Columbia  University  Studies  in  English. 

Columbia  University  Geological  Series. 

Columbia  University  Germanic  Studies. 

Columbia  University  Indo-Iranian  Series. 

Columbia    University   Contributions    to    Oriental    History   and 
Philology. 

Columbia  University  Oriental  Studies. 

Columbia  University  Studies  in  Romance  Philology  and  Liter- 
ature. 

Blumenthal  Lectures.  Hewitt  Lectures. 

Carpentier  Lectures.  Jesup  Lectures. 

Catalogues  will  be  sent  free  on  application. 


THE    MACMILLAN    COMPANY,  AGENTS 

64-66  FIFTH  AVENUE,  NEW  YOKE 


THE  COLUMBIA  UNIVERSITY  PRESS 

Columbia  University  in  the  City  of  New  York 


Sooks  published  at  net  prices  are  sold  by  booksellers  everywhere  at  the  advertised 
net  prices.  When  delivered  from  the  publishers,  carriage,  either  postage  or 
eeopressape,  is  an  extra  charge. 

COLUMBIA   UNIVERSITY   LECTURES 


BLUMENTHAL  LECTURES 

POLITICAL   PROBLEMS  OF   AMERICAN  DEVELOPMENT. 

By  ALBERT  SHAW,  LL.D.,   Editor   of  the   Review  of 
Reviews.     12mo,  cloth,  pp.  vii  +  268.     Price,  $1.50  net. 

CONSTITUTIONAL  GOVERNMENT  IN  THE  UNITED 
STATES.  By  WOODROW  WILSON,  LL.D.,  President 
of  Princeton  University.  12mo,  cloth,  pp.  vii  +  236. 
Price,  $1.50  net. 

THE  PRINCIPLES  OF  POLITICS  FROM  THE  VIEWPOINT 
OF  THE  AMERICAN  CITIZEN.  By  JEREMIAH  W. 
JENKS,  LL.D.,  Professor  of  Political  Economy  and 
Politics  in  Cornell  University.  12mo,  cloth,  pp.  xviii 
+  187.  Price,  $1.50  net. 

HEWITT  LECTURES 

THE  PROBLEM  OF  MONOPOLY.  A  Study  of  a  Grave 
Danger  and  the  Means  of  Averting  it.  By  JOHN 
BATES  CLARK,  LL.D.,  Professor  of  Political  Economy, 
Columbia  University.  12mo,  cloth,  pp.  vi  +  128. 
Price,  $1.25  net. 

JESUP  LECTURES 

LIGHT.  By  KICHARD  C.  MACLAURIN,  LL.D.,  Sc.D.,  Presi- 
dent of  the  Massachusetts  Institute  of  Technology. 
12mo,  cloth.  Price,  $1.50  net. 


THE  MACMILLAN  COMPANY,  AGENTS 

64-66   FIFTH   AVENUE,    NEW   YORK 


